PRESENTED  BY 

PROF.  CHARLES  A.  KOFOID  AND 
MRS.  PRUDENCE  W.  KOFOID 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 


The  Great  Telescope  of  tho  Lick  Observatory.    Aperture,  36  inches;  Length,  57  feet. 


LESSONS    IN    ASTRONOMY 


INCLUDING  URANOGRAPHY 


A   BEIEF    INTEODUCTOEY   COUESE 


WITHOUT  MATHEMATICS 


FOR   USE  IN   SCHOOLS   AND   SEMINARIES 


BY 


CHARLES  A.  YOUNG,  PH.D.,  LL.D. 

PROFESSOR  OF  ASTRONOMY  IN  THE  COLLEGE  OF  NEW  JERSEY  (PRINCETON), 

AUTHOR  OF  A  "  GENERAL  ASTRONOMY  FOR  COLLEGES  AND  SCIENTIFIC 

SCHOOLS,"  AND  OF  "  ELEMENTS  OF  ASTRONOMY  FOR 

HIGH  SCHOOLS  AND  ACADEMIES." 


BOSTON,  U.S.A.,  AND  LONDON 

GINN  AND   COMPANY,   PUBLISHERS 

1891 


VI  PREFACE. 

It  has  been  thought  wejl  also  to  add  brief  notes  on  the  legen- 
dary mythology  of  the  constellations  for  the  benefit  of  such 
pupils  as  are  not  likely  to  become  familiar  with  it  in  the  study 
of  classical  literature. 

In  the  preparation  of  the  book  great  pains  have  been  taken 
not  to  sacrifice  accuracy  and  truth  to  compactness ;  and  no  less 
to  bring  everything  thoroughly  down  to  date.  The  student 
will  find  in  their  proper  places  the  new  results  obtained  by 
Schiaparelli  with  respect  to  the  rotation  of  Mercury  and 
Venus ;  the  identification  of  Brooks's  comet  with  the  long-lost 
comet  of  Lexell,  and  the  latest  spectroscopic  discoveries  of 
Pickering  and  Vogel. 

The  Appendix  contains  in  its  first  chapter  descriptions  of 
the  most  used  astronomical  instruments,  and  where  time  per- 
mits, might  profitably  be  brought  into  the  course.  The  sec- 
ond chapter  of  the  Appendix  is  designed  only  for  the  use  of 
teachers  and  the  more  advanced  pupils.  Arts.  431-434,  how- 
ever, explaining  how  the  sun's  distance  may  be  found  in  the 
simplest  way,  might  well  be  read  by  all. 

My  warmest  thanks  are  due  to  my  friend  and  assistant,  Mr. 
Taylor  Reed,  who  has  gone  over  all  the  proofs  of  the  book, 
and  has  given  me  many  valuable  suggestions. 


CONTENTS. 


PAGE  8 

CHAPTER  I.  —  INTRODUCTION  :  Fundamental  Notions  and  Defi- 
nitions.— The  Celestial  Sphere  and  its  Circles.  —  Altitude 
and  Azimuth.  —  Right  Ascension  and  Declination.  —  Celestial 
Latitude  and  Longitude 1-16 

CHAPTER  II.  —  URANOGRAPHY  :  Globes  and  Star- maps.  —  Star 
Magnitudes.  —  Names  and  Designations  of  Stars.  —  The  Con- 
stellations in  Detail  17-54 

CHAPTER  III.  —  FUNDAMENTAL  PROBLEMS  :  Latitude  and  the 
Aspect  of  the  Celestial  Sphere.  —  Time,  Longitude,  and  the 
Place  of  a  Heavenly  Body .  55-67 

CHAPTER  IV.  —  THE  EARTH  :  Its  Form  and  Dimensions  ;  its 
Rotation,  Mass,  and  Density;  its  Orbital  Motion  and  the 
Seasons.  —  Precession.  —  The  Year  and  the  Calendar  .  .  68-90 

CHAPTER  V.  —  THE  MOON  :  Her  Orbital  Motion  and  the  Month. 

—  Distance,  Dimensions,  Mass,  Density,  and  Force  of  Grav- 
ity. —  Rotation  and  Librations.  — Phases.  — Light  and  Heat. 

—  Physical  Condition.  —  Telescopic  Aspect  and  Surface  .        .  91-110 

CHAPTER  VI.  — THE  SUN:  Its  Distance,  Dimensions,  Mass,  and 
Density.  —  Its  Rotation,  Surface,  and  Spots.  —  The  Spectro- 
scope and  the  Solar  Spectrum  ;  the  Chemical  Constitution  of 
the  Sun.  —  The  Chromosphere  and  Prominences.  —  The  Cor- 
ona. —  The  Sun's  Light.  —  Measurement  and  Intensity  of  the 
Sun's  Heat.  — Theory  of  its  Maintenance,  and  Speculations 
regarding  the  Age  and  Duration  of  the  Sun  .  .  .  111-141 

vii 


Vlll  CONTENTS. 


CHAPTER  VII.  —  ECLIPSES  AND  THE  TIDES  :  Form  and  Dimen- 
sions of  Shadows.  —  Eclipses  of  the  Moon.  —  Solar  Eclipses, 
Total,  Annular,  and  Partial.  —  Number  of  Eclipses  in  a  Year. 
—  Recurrence  of  Eclipses,  and  the  Saros.  —  Occupations.  — 
The  Tides 142-156 

CHAPTER  VIII.  — THE  PLANETARY  SYSTEM:  The  Planets  in 
General.  —  Their  Number,  Classification,  and  Arrangement.  — 
Bode's  Law.  —  Orbits  of  the  Planets.  —  Kepler's  Laws  and 
Gravitation.  —  The  Apparent  Motions  of  the  Planets  and  the 
Systems  of  Ptolemy  and  Copernicus.  —  Determination  of  the 
Planets'  Diameters,  Masses,  etc.  —  Herschel's  Illustration  of 
the  System.  —  Description  of  Individual  Planets  :  the  '  Ter- 
restrial '  Planets,  Mercury,  Venus,  and  Mars  .  .  .  157-186 

CHAPTER  IX.  —  PLANETS  (continued}  :  The  Asteroids.  —  Intra- 
Mercurian  Planets  and  the  Zodiacal  Light.  —  The  Major  Plan- 
ets, Jupiter,  Saturn,  Uranus,  and  Neptune.  — Ultra- Neptunian 
Planet  187-207 

CHAPTER  X.  —  COMETS  AND  METEORS  :  Comets,  their  Num- 
ber, Designation,  and  Orbits  ;  their  Constituent  Parts  and 
Appearance  ;  their  Spectra,  Physical  Constitution,  and  Proba- 
ble Origin ;  Remarkable  Comets  ;  Aerolites,  their  Fall  and 
Characteristics  ;  Shooting  Stars  and  Meteoric  Showers  ;  Con- 
nection between  Meteors  and  Comets  ....  208-242 

CHAPTER  XL  —  THE  STARS  :  Their  Nature,  Number,  and  Des- 
ignation. —  Star  Catalogues  and  Charts.  —  Their  Proper 
Motions,  and  the  Motion  of  the  Sun  in  Space.  —  Stellar  Par- 
allax. —  Star  Magnitudes  and  Photometry.  —  Variable  Stars. 
—Stellar  Spectra  . 243-266 

CHAPTER  XII.  —  THE  STARS  (continued)  :  Double  and  Multi- 
ple Stars  ;  Clusters  and  Nebulae  ;  the  Milky  Way,  and  Distri- 
bution of  Stars  in  Space  ;  the  Stellar  Universe.  —  Cosmogony 
and  the  Nebular  Hypothesis 267-293 


CONTENTS.  IX 


APPENDIX. 

PAGES 

CHAPTER  XIII. —ASTRONOMICAL  INSTRUMENTS:  The  Telescope, 
Simple  Refracting,  Achromatic,  and  Reflecting.  —  The  Equa- 
torial. —  The  Filar  Micrometer.  —  The  Transit  Instrument.  — 
The  Clock  and  the  Chronograph.  —The  Meridian  Circle.  — 
The  Sextant 295-312 

CHAPTER  XIV.  (FOR  THE  MOST  PART  SUPPLEMENTARY  TO  ARTI- 
CLES IN  THE  TEXT).  —  Hour-angle  and  Time.  —  Twilight. — 
Determination  of  Latitude.  —  Place  of  a  Ship  at  Sea.  —  Find- 
ing the  Form  of  the  Earth's  Orbit.  —The  Ellipse.  —  Illustra- 
tions of  Kepler's  '  Harmonic '  Law.  —  The  Equation  of  Light, 
and  the  Sun's  Distance  determined  by  it.  —  Aberration  of 
Light.  -De  1'Isle's  Method  of  getting  the  Sun's  Parallax  from 
a  Transit  of  Venus.  —  The  Parabola  and  the  Conic  Sections. 
—  Determination  of  Stellar  Parallax.  —  The  Slitless  Spectro- 
scope    313-331 

QUESTIONS  FOR  REVIEW 332 

TABLES   OF  ASTRONOMICAL   DATA: 

I.  Astronomical  Constants 339 

II.  The  Principal  Elements  of  the  Solar  System    ...  340 

III.  The  Satellites  of  the  Solar  System 341 

IV.  The  Principal  Variable  Stars 342 

V.  The  Best  Determined  Stellar  Parallaxes    ....  343 

VI.  The  Greek  Alphabet  and  Miscellaneous  Symbols      .        .        344 

INDEX 345 

STAR-MAPS  359 


CHAPTER  I. 

INTRODUCTION.  —  FUNDAMENTAL  NOTIONS  AND  DEFINI- 
TIONS. —  THE  CELESTIAL  SPHERE  AND  ITS  CIRCLES. 
—  ALTITUDE  AND  AZIMUTH.  —  RIGHT  ASCENSION  AND 
DECLINATION.  —  CELESTIAL  LATITUDE  AND  LONGITUDE. 

1.  ASTRONOMY1  is  the  science  which  deals  with  the  heavenly 
bodies. 

As  it  is  the  oldest  of  the  sciences,  so  also  it  is  one  of  the 
most  perfect,  and  in  certain  aspects  the  noblest,  as  being  the 
most  "  unselfish  "  of  them  all.  And  yet,  although  not  bearing 
so  directly  upon  the  material  interests  of  life  as  the  more 
modern  sciences  of  Physics  and  Chemistry,  it  is  of  high  utility. 
By  means  of  Astronomy  the  latitudes  and  longitudes  of  places 
upon  the  earth's  surface  are  determined,  and  by  such  determi- 
nations alone  is  it  possible  to  conduct  vessels  upon  the  sea. 
Moreover,  all  the  operations  of  surveying  upon  a  large  scale, 
such  as  the  determination  of  the  boundaries  of  countries,  de- 
pend more  or  less  upon  astronomical  observations.  The  same 
is  true  of  operations  which,  like  the  railway  service,  require 
an  accurate  knowledge  and  observance  of  time ;  for  the  funda- 
mental timekeeper  is  the  diurnal  revolution  of  the  heavens,  as 
determined  by  the  astronomer's  transit-instrument. 

In  ancient  times  the  science  was  supposed  to  have  a  still  higher 
utility.  It  was  believed  that  human  affairs  of  every  kind,  the  welfare 
of  nations,  and  the  life  history  of  individuals  alike,  were  controlled, 

1  The  term  is  derived  from  two  Greek  words :  astron,  a  star,  and 
wornos,  a  law. 

1 


2  THE   HEAVENLY   BODIES.  [§  1 

or  at  least  prefigured,  by  the  motions  of  the  stars  and  planets ;  so 
that  from  the  study  of  the  heavens  it  ought  to  be  possible  to  predict 
futurity. 

2.  The  heavenly  bodies  include,  first,  the  solar  system,  — 
that  is,  the  sun  and  the  planets  which  revolve  around  it,  with 
their  attendant  satellites ;  second,  the  comets  and  the  meteors, 
which  also  revolve  around  the  sun,  but  are  bodies  of  a  very 
different  nature  from  the  planets,  and  move  in  different  kinds 
of  orbits ;  and,  thirdly,  the  stars  and  nebulae.     The  earth  on 
which  we  live  is  one  of  the  planets,  and  the  moon  is  the  earth's 
satellite.     The  stars  which  we  see  are  bodies  of  the  same  kind 
as  the  sun,  shining  like  him  with  fiery  heat,  while  the  planets 
and  the  satellites  are  dark  and  cool  like  the  earth,  and  visible 
to  us  only  by  the  sunlight  they  reflect.    As  for  the  comets  and 
nebulae,  they  appear  to  be  mere  clouds,  composed  of  heated  gas 
or  swarms  of  little  particles  of  more  solid  substances,  perhaps 
not  very  hot,  but  luminous  from  some  cause  or  other.     It  is 
likely  that  besides  the  visible  stars  there  are  also  multitudes 
which,  although  too  cool  to  shine,  manifest  their  existence  by 
affecting  the  motion  of  certain  of  the  stars  which  we  can  see. 
It  is  hardly  necessary  to  add  that  while  with  the  naked  eye 
we  see  only  a  few  thousand  stars,  the  telescope  makes  millions 
visible. 

3.  As  we  look  off  from  the  earth  at  night,  the  stars  appear 
to  be  all  around  us,  like  glittering  points  fastened  to  the  inside 
of  a  huge  hollow  globe.     Really  they  are  at  very  different  dis- 
stances,  all  enormous  as  compared  with  any  distances  with 
which  geography  makes  us  familiar.     Even  the  moon  is  eighty 
times  as  far  away  as  New  York  from  Liverpool,  and  the  sun 
is  nearly  four  hundred  times  as  distant  as  the  moon,  and  the 
nearest  of  the  stars  is  more  than  two  hundred  thousand  times 
as  distant  as  the  sun ;  as  to  the  remoter  stars,  some  of  them 
are  certainly  thousands  of  times  as  far  away  as  the  nearer 
ones,  —  so  far  that  light  itself  is  thousands  of  years  in  coming 


§  3]  THE   HEAVENLY   BODIES. 

to  us  from  them.     These  are  facts  which  are  certain,  not  mere 
guesses  or  beliefs. 

Then,  too,  as  to  their  motions.  Although  the  heavenly  bodies 
seem  to  us  for  the  most  part  to  be  at  rest,  except  as  the  earth's 
rotation  makes  them  appear  to  rise  and  set,  yet  really  they  are 
all  moving,  and  with  a  swiftness  of  which  we  can  form  no  con- 
ception. A  cannon-ball  is  a  snail  to  the  slowest  of  them.  The 
earth  itself  in  its  revolution  around  the  sun  is  flying  eighteen 
and  a  half  miles  in  a  second,  which  is  more  than  fifty  times  as 
fast  as  the  swiftest  rifle  bullet.  We  fail  to  perceive  the  motion 
simply  because  it  is  so  smooth  and  so  unresisted.  The  space 
outside  our  air  contains  nothing  that  can  sensibly  obstruct 
either  sight  or  motion. 

4.  But  this  knowledge  as  to  the  real  distance  and  motions 
of  the  heavenly  bodies  was  gained  only  after  long  centuries  of 
study.  If  we  go  out  to  look  at  the  stars  some  moonless  night 
we  find  them  apparently  sprinkled  over  the  dome  of  the  sky 
in  groups  or  constellations,  which  are  still  substantially  the 
same  as  in  the  days  of  the  earliest  astronomers.  At  first  these 
constellations  were  figures  of  animals  and  other  objects,  and 
many  celestial  globes  and  maps  still  bear  grotesque  pictures 
representing  them.  At  present,  however,  a  constellation  is 
only  a  certain  region  of  the  sky,  limited  by  imaginary  lines 
which  divide  it  from  the  neighboring  constellations,  just  as 
countries  are  divided  in  geography.  As  to  the  exact  boun- 
daries of  these  constellations,  and  even  their  number,  there  is 
no  precise  agreement  among  astronomers.  Forty-eight  of  them 
have  come  down  to  us  from  the  time  of  Ptolemy,1  and  even  in 
his  day  many  of  them  were  already  ancient. 

About  twenty  more,  which  have  been  proposed  by  more 
recent  astronomers,  are  now  recognized,  besides  a  considerable 
number  which  have  been  abandoned. 

1  Ptolemy,  the  greatest  astronomer  of  antiquity,  flourished  at  Alexan- 
dria about  130  A.D. 


4  UKANOGRAPHY.  [§  5 

5.  TTranography,  or  Description  of  the  Visible  Heavens.  — 

The  study  of  the  constellations,  or  the  apparent  arrangement 
of  the  stars  in  the  sky,  is  called  Uranography.1  It  is  not  an 
essential  part  of  Astronomy,  but  it  is  an  easy  and  pleasant 
study ;  and  in  becoming  familiar  with  the  constellations  and 
their  principal  stars,  the  pupil  will  learn  more  readily  and 
thoroughly  than  in  any  other  way  the  most  important  facts  in 
relation  to  the  apparent  motions  of  the  heavenly  bodies,  and 
the  principal  points  and  circles  of  the  celestial  sphere.  For 
this  reason  the  teacher  is  urged  to  take  the  earliest  oppor- 
tunity to  have  his  pupils  trace  such  of  the  constellations  as 
happen  to  be  visible  in  the  evening  sky  when  they  begin  the 
study  of  Astronomy. 

6.  The  Celestial  Sphere.2  —  The  sky  appears  like  a  hollow 
vault,  to  which  the  stars  seem  to  be  attached,  like  specks  of 
gilding  upon  the  inner  surface  of  a  dome.     We  cannot  judge 
of  the  distance  of  this  surface  from  the  eye,  further  than  to 
perceive  that  it  must  be  very  far  away.    It  is  therefore  natural 
and  extremely  convenient  to  regard  the  distance  of  the  sky  as 
everywhere  the  same  and  unlimited.     The  '  celestial  sphere,'  as 
it  is  called,  is  conceived  of  as  so  enormous  that  the  whole  world 
of  stars  and  planets  lies  in  its  centre  like  a  few  grains  of  sand 
in  the  middle  of  the  dome  of  the  Capitol.     Its  diameter  is 
assumed  to  be  immeasurably  greater  than  any  actual  distance 
known,  and  greater  than  any  quantity  assignable.    In  technical 
language  it  is  taken  as  mathematically  infinite. 

Since  the  celestial  sphere  is  thus  infinite,  any  two  parallel 
lines  drawn  from  distant  points  on  the  surface  of  the  earth,  or 
even  from  points  as  distant  as  the  earth  and  the  sun,  will  seem 
to  meet  at  one  point  on  the  surface  of  the  sphere.  If  the  two 

1  From  the  Greek,  ouranos  (heavens),  and  graphe  (description). 

2  The  study  of  the  celestial  sphere  and  its  circles  is  greatly  facilitated 
by  the  use  of  a  globe,  or  armillary  sphere.     Without  some  such  appa- 
ratus it  is  not  easy  for  a  young  person  to  get  clear  ideas  upon  the  subject. 


D 


§  6]  APPARENT   PLACE  OF  A   HEAVENLY  BODY.  5 

lines  were  anywhere  a  million  miles  apart,  for  instance,  they 
will,  of  course,  still  be  a  million  miles  apart  when  they  reach 
the  surface  of  the  sphere ;  but  at  an  infinite  distance  even  a 
million  miles  is  a  mere  nothing,  so  that  the  two  lines  make 
apparently  but  a  single  point1  where  they  pierce  the  sphere. 

7.  The  Apparent  Place  of  a  Heavenly  Body.  —  This  is  sim- 
ply the  point  where  a  line  drawn  from  the  observer  through 
the  body  in  question,  continued 

outward,  pierces  the  celestial 
sphere.  It  depends  solely  upon 
the  direction  of  the  body,  and 
is  in  no  way  affected  by  its  dis- 
tance from  us.  Thus,  in  Fig.  1, 
A,  B,  (7,  etc.,  are  the  apparent 
places  of  a,  b,  c,  etc.,  the  observ- 
er being  at  0.  Objects  that  are 
nearly  in  line  with  each  other, 
as  Jiy  i,  k,  will  appear  close  to- 
gether. The  moon,  for  instance, 
often  looks  to  us  very  near  a  star,  which  is  really  of  course  at 
an  enormous  distance  beyond  her. 

8.  Angular  Measurement.  —  It  is  clear  that  we  cannot  prop- 
erly describe  the  apparent  distance  of  two  points  upon  the 
celestial  sphere  from  each  other  by  feet  or  inches.     To  say 
that  two  stars  are  about  five  feet  apart,  for  instance,  —  and  it 
is  not  very  uncommon  to  hear  such  an  expression,  —  means 
nothing  unless  we  know  how  far  from  the  eye  the  five-foot 
measure  is  to  be  held.     The  proper  units  for  expressing  appar- 
ent distance  in  the  sky  are  those  of  angle,  viz. :  degrees  (°), 
minutes   (f),  and  seconds  (")  ;  the  circumference  of  a  circle 
being  divided  into  360  degrees,  each  degree  into  60  minutes, 
and  each  minute  into  60  seconds.     Thus,  the  Great  Bear's  tail, 


FIG.  i. 


1  This  is  the  same  as  the  '  vanishing-point '  of  perspective. 


6  CIRCLES   OF   THE   CELESTIAL   SPHERE.  [§  8 

or  Dipper-handle,  is  about  16°  long,  and  the  long  side  of  the 
Dipper-bowl  is  about  10°;  the  moon  and  the  sun  are  each 
about  half  a  degree,  or  30',  in  diameter. 

It  is  very  important  that  the  student  in  Astronomy  should  become 
accustomed  as  soon  as  possible  to  estimate  celestial  measures  in  this 
way.  A  little  practice  soon  makes  it  easy,  though  at  first  one  is  apt 
to  be  embarrassed  by  the  fact  that  the  sky  looks  to  the  eye  not  like  a 
true  hemisphere  but  like  a  flattened  vault,  so  that  the  estimates  of 
distances  for  all  objects  near  the  horizon  are  apt  to  be  too  large.  The 
moon,  when  rising  or  setting,  looks  to  most  persons  much  larger  than 
when  overhead ;  and  the  Dipper-bowl,  when  underneath  the  pole,  seems 
to  cover  s^much  larger  area  than  when  above  it. 

9.  Circles  and  Principal  Points  of  the  Celestial  Sphere. — 

Just  as  the  surface  of  the  earth  in  Geography  is  covered  with 
a  net-work  of  imaginary  lines, — meridians  and  parallels  of 
latitude,  —  so  the  sky  is  supposed  to  be  marked  off  in  a  some- 
what similar  way.  Two  such  sets  of,,,  points  and  reference 
circles  are  in  common  use  to  describe  the  apparent  places  of 
the  stars,  and  a  third  was  used  by  the  ancients  and  is  still  em- 
ployed for  some  purposes.  The  first  system  depends  upon  the 
direction  of  the  force  of  gravity  shown  by  a  plumb-line  at  the 
point  where  the  observer  stands ;  the  second  upon  the  direc- 
tion of  the  axis  of  the  earth,  which  points  very  near  the  so- 
called  Pole-star ;  and  the  third  depends  upon  the  position  of 
the  orbit  in  which  the  earth  travels  around  the  sun. 

10.  The  Gravitational  or  Up-and-Down  System.  —  (a)  The 

Zenith  and  Nadir.  The  point  in  the  sky  directly  above  the 
observer  is  called  the  zenith;  the  opposite  point,  under  the 
earth  and  of  course  invisible,  the  nadir.1 

(b)     The   Horizon    (pronounced   ho-ri'-zon,  not   hor'-i-zon). 

1  These  are  Arabic  terms.  About  1100  A.D.  the  Arabs  were  the 
world's  chief  astronomers,  and  have  left  their  mark  upon  the  science  in 
numerous  names  of  stars  and  astronomical  terms. 


10] 


VERTICAL   CIRCLES. 


This  is  a  l  great  circle  '  *  around  the  sky,  half-way  between  the 
zenith  and  the  nadir,  and  therefore  everywhere  90°  from  the 
zenith.  The  word  is  derived  from  a  Greek  word  which  means 
a  'boundary';  i.e.,  the  line  where  the  earth  or  sea  limits  the 
sky.  The  actual  line  of  division,  which  on  the  land  is  always 
more  or  less  irregular,  is  called  the  visible  horizon,  to  distin- 
guish it  from  the  true  horizon  denned  above.  We  may  also 
define  the  horizon  as  the  great  circle  where  a  plane  which 
passes  through  the  observer's  eye  perpendicular  to  the  plumb- 
line  cuts  the  celestial  sphere. 

11.  Vertical  Circles  and  the  Meridian;  Altitude,  and  Azi- 
muth. —  Circles  drawn  from  the  zenith  to  the  nadir  cut  the 
horizon  at  right  angles,  and  are  known  as  vertical  circles.  Each 
star  has  at  any  moment  its  own  vertical  circle. 


FIG.  2.  — The  Horizon  and  Vertical  Circles. 


O,  the  place  of  the  Observer. 
OZ,  the  Observer's  Vertical. 
Z,  the  Zenith;  P,  the  Pole. 
S  WNE,  the  Horizon. 
SZPN,  the  Meridian. 
EZW,  the  Prime  Vertical. 


M,  some  Star. 

ZMH,  arc  of  the  Star's  Vertical  Circle. 

TMIt,  the  Star's  Almucantar. 

Angle  TZM,  or  arc  Sff,  Star's  Azimuth. 

Arc  HM,  Star's  Altitude. 

Arc  ZM,  Star's  Zenith  Distance. 


That  particular  vertical  circle  which  passes  north  and  south 
is  known  as  the  celestial  MEKIDIAN  ;  while  the  vertical  circle 
at  right  angles  to  this  is  called  the  prime  vertical.  Small  circles 


1  '  Great  Circles '  are  those  which  divide  the  sphere  into  two  equal 
parts. 


8  DIURNAL   ROTATION.  [§  H 

drawn  parallel  to  the  horizon  are  known  as  parallels  of  alti- 
tude. Fig.  2  illustrates  these  circles. 

By  their  help  we  can  easily  define  the  apparent  position  of 
a  heavenly  body. 

Its  Altitude  is  its  apparent  elevation  above  the  horizon ;  that 
is,  the  number  of  degrees  between  it  and  the  horizon  measured 
on  a  vertical  circle.  Thus,  in  Fig.  2,  the  vertical  circle  ZMH 
passes  through  the  point  M.  The  arc  MH9  measured  in 
degrees,  is  the  altitude  of  M,  and  the  arc  ZM  is  called  its 
zenith  distance. 

The  Azimuth  of  a  heavenly  body  is  the  same  as  its  '  bearing ' 
in  Surveying,  but  measured  from  the  true  meridian  and  not 
from  the  magnetic.1  It  is  the  arc  of  the  horizon,  measured  in 
degrees,  intercepted  between  the  south  point  and  the  foot  of 
the  vertical  circle  which  passes  through  the  object. 

There  are  various  ways  of  reckoning  azimuth.  Many  writ- 
ers express  it  in  the  same  way  as  the  'bearing7  in  Surveying, 
i.e.,  so  many  degrees  east  or  west  of  north  or  south.  In  the 
figure,  the  azimuth  of  M  thus  expressed  is  about  S,  50°  E. 
The  more  usual  way  at  present,  however,  is  to  reckon  clear 
around  from  the  south,  through  the  west,  to  the  point  of  be- 
ginning. Expressed  in  this  way  the  azimuth  of  M  would  be 
about  310°,  —  i.e.,  the  arc  8  WNEH. 

Altitude  and  azimuth,  however,  are  inconvenient  for  many 
purposes,  because  they  continually  change  for  a  celestial  object 
as  it  moves  across  the  sky. 

12,  The  Apparent  Diurnal  Rotation  of  the  Heavens. — If  we 

go  out  on  some  clear  evening  in  the  early  autumn,  say  about 
the  22d  of  September,  and  face  the  north,  we  shall  find  the  ap- 
pearance of  that  part  of  the  heavens  directly  before  us  substan- 
tially as  shown  in  Fig.  3.  In  the  north  is  the  constellation  of 

1  The  reader  is  reminded  that  the  magnetic  needle  does  not  point 
exactly  north.  Its  direction  varies  widely  at  different  parts  of  the  earth, 
and,  moreover,  is  continually  changing  to  some  extent. 


§12] 


DIURNAL  ROTATION. 


9 


the  Great  Bear  (Ursa  Major),  characterized  by  the  conspicuous 
group  of  seven  stars  known  as  the  "  Great  Dipper.'7  It  now 
lies  with  its  handle  sloping  upward  to  the  west.  The  two 
easternmost  stars  of  the  four  which  form  its  bowl  are  called 


FIG.  3.  —  The  Northern  Circumpolar  Constellations. 

the  "  Pointers,"  because  they  point  to  the  Pole-star,  which  is  a 
solitary  star  not  quite  half-way  from  the  horizon  to  the  zenith 
(in  the  latitude  of  New  York),  and  about  as  bright  as  the 
brighter  of  the  two  Pointers. 

High  up  on  the  opposite  side  of   the  Pole-star   from  the 
Great  Dipper,  and  at  nearly  the  same  distance,  is  an  irregular 


10  DIURNAL   ROTATION.  [§  12 

zigzag  of  five  stars,  each  about  as  bright  as  the  Pole-star  itself.. 
This  is  the  constellation  of  Cassiopeia. 

If  now  we  watch  these  stars  for  only  a  few  hours,  we  shall 
find  that  while  all  the  forms  remain  unaltered,  their  places  in 
the  sky  are  slowly  changing.  The  Great  Dipper  slides  down- 
ward towards  the  north,  so  that  by  eleven  o'clock  (on  Sept. 
22)  the  Pointers  are  directly  under  the  Pole-star.  Cassiopeia 
still  keeps  opposite^  however,  rising  towards  the  zenith ;  and 
if  we  continue  the  watch  through  the  whole  night,  we  shall 
find  that  all  the  stars  appear  to  be  moving  in  circles  around  a 
point  near  the  Pole-star,  revolving  in  the  opposite  direction  to 
the  hands  of  a  watch  (as  we  look  towards  the  north)  with  a 
steady  motion  which  takes  them  completely  around  once  a  day, 
or,  to  be  more  exact,  once  in  23h  56m  4.1s  of  ordinary  time. 
They  behave  just  as  if  they  were  attached  to  the  inner  surface 
of  a  huge  revolving  sphere. 

To  indicate  the  position  of  the  stars  as  it  will  be  at  midnight  of 
Sept.  22,  the  figure  must  be  held  so  that  XII  in  the  margin  is  at  the 
bottom;  at  4  A.M.  the  stars  will  have  come  to  the  position  indicated 
by  bringing  XVI  to  the  bottom,  and  so  on.  But  at  eight  o'clock  on 
the  next  night  we  shall  find  things  in  their  original  position  very 
nearly. 

If  instead  of  looking  toward  the  north  we  now  look  south- 
ward, we  shall  find  that  in  that  part  of  the  sky  also  the  stars 
appear  to  move  in  the  same  kind  of  way.  All  that  are  not  too 
near  the  Pole-star  rise  somewhere  in  the  eastern  horizon, 
ascend  obliquely  to  the  meridian,  and  descend  to  their  setting 
at  points  on  the  western  horizon.  The  next  day  they  rise  and 
set  again  at  precisely  the  same  points,  and  the  motion  is 
always  in  an  arc  of  a  circle,  called  the  star's  diurnal  circle,  the 
size  of  which  depends  upon  its  distance  from  the  pole.  More- 
over, all  of  these  arcs  are  strictly  concentric. 

The  ancients  accounted  for  these  fundamental  and  obvious 
facts  by  supposing  that  the  stars  are  really  fastened  to  the 


§  12]  DEFINITION   OF   THE   POLES.  11 

celestial  sphere,  and  that  this  sphere  really  turns  daily  in  the 
manner  indicated.  According  to  this  view  there  must  really 
be  upon  the  sphere  two  opposite  points  which  remain  at  rest, 
and  these  are  the  poles. 

13.  Definition  of  the  Poles.  —  The  Poles,  therefore,  may  be 
denned  as  those  two  points  in  the  sky  where  a  star  would  have 
no  diurnal  motion.     The  exact  position  of  either  pole  may  be 
determined  with  proper  instruments,  by  finding  the  centre  of 
the  small  diurnal  circle  described  by  some  star  near  it,  as,  for 
instance,  by  the  Pole-star. 

The  student  must  be  careful  not  to  confound  the  Pole  with 
the  Pole-star..  The  pole  is  an  imaginary  point;  the  Pole- 
star  is  only  that  one  of  the  conspicuous  stars  which  happens 
now  to  be  nearest  to  that  point.  The  Pole-star  at  present  is 
about  1£°  distant  from  it.  If  we  draw  an  imaginary  line  from 
the  Pole-star  to  the  star  Mizar  (the  one  at  the  bend  of  the 
Dipper-handle),  it  will  pass  almost  exactly  through  the  pole 
itself ;  the  distance  of  the  pole  from  the  Pole-star  being  very 
nearly  one-quarter  of  the  distance  between  the  two  "Pointers." 

This  definition  of  the  pole  is  that  which  would  be  given  by 
one  familiar  with  the  sky,  but  ignorant  of  the  earth's  rotation, 
and  it  is  still  perfectly  correct ;  but  knowing,  as  we  now  do, 
that  this  apparent  revolution  of  the  celestial  sphere  is  due  to 
the  real  spinning  of  the  earth  on  its  axis,  we  may  also  define 
the  poles  as  the  two  points  where  the  earths  axis  of  rotation, 
produced  indefinitely,  would  pierce  the  celestial  sphere. 

Since  the  two  poles  are  diametrically  opposite  in  the  sky,  only  one 
of  them  is  usually  visible  from  any  given  place.  Observers  north  of 
the  earth's  equator  see  only  the  north  pole,  and  vice  versa  for  observ- 
ers in  the  southern  hemisphere. 

14.  The  Celestial  Equator,  or  Equinoctial;  Declination. — 

The  Equator  is  a  great  circle  of  the  celestial  sphere  drawn 
half-way  between  the  poles,  everywhere  90°  from  each  of  them, 


12  HOUR-CIRCLES.  [§  14 

and  is  the  great  circle  in  which,  the  plane  of  the  earth's  equator 
cuts  the  celestial  sphere.  It  is  often  called  the  Equinoctial. 
Fig.  4  shows  how  the  plane  of  the  earth's  equator  produced 
far  enough  would  mark  out  such  a  circle  in  the  heavens. 

Small  circles  drawn  parallel 
to  the  equinoctial,  like  the  paral- 
lels of  latitude  on  the  earth,  are 
known  as  'Parallels  of  Decli- 
nation,' the  Declination  of  a  star 
being  its  distance  in  degrees 
north  or  south  of  the  celestial 
equator,  +  if  north,  —  if  south. 
It  corresponds  precisely  with 
the  latitude  of  a  place  on  the 
earth's  surface ;  but  it  cannot  be 
FIG.  4.  — The  riane  of  the  Earth's  Equa-  called  celestial  latitude,  because 
tor  produced  to  cut  the  CeieBtiai  Sphere.  that  term  has  been  preoccupied 

for  an  entirely  different  quantity  (Art.  20).  A  star's  parallel 
of  declination  is  identical  with  its  diurnal  circle. 

15.  Hour-circles.  —  The  great  circles  of  the  celestial  sphere 
which  pass  through  the  poles  like  the  meridians  on  the  earth, 
and  are  therefore  perpendicular  to  the  celestial  equator,  are 
called  Hour-Circles.     Some  writers  call  them  celestial  merid- 
ians, but  the  term  is  objectionable  since  it  is  sometimes  used 
to  indicate  an  entirely  different  set  of  circles.     That  particu- 
lar hour-circle  which  at  any  moment  passes  through  the  zenith 
of  course  coincides  with  the  celestial  meridian  already  defined 
in  Art.  11. 

16.  The  Celestial  Meridian  and  the  Cardinal  Points.  —  The 

best  definition  of  the  celestial  meridian  is,  however,  the  great 
circle  which  passes  through  the  zenith  and  the  poles.  The  points 
where  this  meridian  cuts  the  horizon  (the  circle  of  level),  are 
the  north  and  south  points,  and  the  east  and  west  points  of 


16] 


THE  VERNAL   EQUINOX. 


13 


the  horizon  lie  half-way  between  them,  the  fonr  being  known 
as  the  "  Cardinal  Points."  The  student  is  especially  cautioned 
against  confounding  the  north  point  with  the  north  pole.  The 
north  point  is  on  the  horizon  ;  the  north  pole  is  high  up  in  the 
sky. 


FIG.  5.  —  Equator,  Hour-Circles,  etc. 


O,  place  of  the  Observer;  Z,  his  Zenith. 

SENW,  the  Horizon. 

POP',  line  parallel  to  the  axis  of  the  Earth. 

P  and  P't  the  two  Poles  of  the  Heavens. 

EQ  WT,  the  Celestial  Equator,  or  Equinoc- 
tial. 

X,  the  Vernal  Equinox,  or  "  First  of 
Aries." 

PXP',  the  Equinoctial  Colure,  or  Zero 
Hour-Circle. 


m,  some  Star. 

Ym,  the  Star's  Declination;  Pm,  its  North- 
Polar  Distance. 

Angle  mPR  =arc  QY,  the  Star's  (eastern) 
Hour-Angle;  =  24h  minus  Star's 
western  Hour- Angle. 

Angle  XPm  =  arc  X Y,  Star's  Right  Ascen- 
sion. 

Sidereal  time  at  the  moment  =  24h  minus 
XPQ. 


In  Fig.  5,  P  is  the  north  celestial  pole,  Z  is  the  zenith,  and 
SQZPN  is  the  celestial  meridian.  P  and  P1  are  the  poles, 
PmP  is  the  hour-circle  of  m,  and  amRb  V  is  its  parallel  of 
declination,  or  diurnal  circle.  N  and  S  are  the  north  and 
south  points  respectively.  In  the  figure,  m  Y  is  the  decimation 
of  m,  and  mP  is  called  its  polar  distance. 

17.  The  Vernal  Equinox,  or  First  of  Aries.  —  In  order  to 
use  this  system  of  circles  as  a  means  of  designating  the  places 


14  RIGHT   ASCENSION.  [§  17 

of  stars  in  the  sky,  it  is  necessary  to  fix  upon  some  one  hour- 
circle,  to  be  reckoned  from  in  the  same  way  that  the  meridian 
of  Greenwich  is  used  on  the  earth's  surface.  The  "Green- 
wich of  the  sky  "  which  has  thus  been  fixed  upon,  is  the  point 
where  the  sun  crosses  the  celestial  equator  in  the  spring. 
The  sun  and  moon  and  the  planets  do  not  behave  as  if  they, 
like  the  stars,  were  firmly  fixed  upon  the  celestial  sphere,  but 
rather  as  if  they  were  glow-worms  crawling  slowly  about  upon 
its  surface  while  it  carries  them  in  its  diurnal  rotation.  As 
every  one  knows,  the  sun  in  winter  is  far  to  the  south  of  the 
equator,  and  in  the  summer  far  to  the  north,  apparently  com- 
pleting a  yearly  circuit  of  the  heavens  on  a  path  known  as  the 
ecliptic.  It  crosses  the  equator,  therefore,  twice  a  year,  pass- 
ing from  the  south  side  of  it  to  the  north  about  March  20th, 
and  always  at  the  same  point  (neglecting  for  the  present  the 
effect  of  what  is  known  as  l  precession ').  This  point  is  called 
the  (  Vernal  Equinox,'  and  is  made  the  starting-point.  Unfor- 
tunately it  is  not  marked  by  any  conspicuous  star ;  but  a  line 
drawn  from  the  Pole-star  through  Beta  Cassiopei'ae  (the  west- 
ernmost or  "  preceding "  star  in  the  zigzag)  (see  Map  I.)  and 
continued  90°  from  the  pole,  strikes  very  near  it.  In  Fig.  5, 
X  represents  this  point.  It  is  often  called  the  "First  of 
Aries." 

18.  Right  Ascension.  —  The  right  ascension  of  a  star  is  the 
arc  of  the  celestial  equator  intercepted  between  the  vernal  equinox 
and  the  point  where  the  star's  hour-circle  cuts  the  equator,  and  is 
reckoned  always  eastward  from  the  equinox  and  completely 
around  the  circle.  It  may  be  expressed  either  in  degrees  or 
in  hours.  A  star  one  degree  west  of  the  equinox  has  a  right 
ascension  of  359°,  or  of  23h  56m.  Evidently  the  diurnal 
motion  does  not  affect  the  right  ascension  of  a  star,  but  this, 
like  the  declination,  remains  practically  unchanged  for  years. 
In  Fig.  5,  if  X  be  the  vernal  equinox  the  right  ascension  of  m 
is  the  arc  XY  measured  from  X  eastward. 


§  19]  SUMMARY.  15 

19.  Thus  we  can  define  the  position  of  a  star  either  by  its 
altitude  and  azimuth,  which  tell  how  high  it  is  in  the  sky,  and 
how   it   "  bears,"  as  a  sailor  would  say ;    or  we  may  use  its 
right   ascension   and  declination,  which  do  not   change  from 
day  to  day  (not  perceptibly  at  least),  and  so  are  better  adapted 
to   mapping  purposes,  corresponding  as  they  do  precisely  to 
latitude  and  longitude  upon  the  surface  of  the  earth. 

Perhaps  the  easiest  way  to  think  of  these  celestial  circles  is 
the  following :  Imagine  a  tall  pole  standing  straight  up  from 
the  observer,  having  attached  to  it  at  the  top  (the  zenith)  two 
half  circles  coming  down  to  the  level  of  the  observer's  eye,  one 
of  them  running  north  and  south  (the  meridian),  and  the 
other  east  and  west  (the  prime  vertical).  The  bottoms  of 
these  two  semicircles  are  connected  by  a  complete  circle,  the 
horizon,  at  the  level  of  the  eye.  This  framework,  immense 
but  fortunately  only  imaginary  and  so  not  burdensome,  the 
observer  takes  with  him  wherever  he  goes,  keeping  always  at 
its  centre,  while  over  it  turns  the  celestial  sphere  ;  more 
strictly,  he  and  the  earth  and  his  framework  turn  together 
under  the  celestial  sphere. 

The  circles  of  the  other  set  are  drawn  upon  the  celestial 
sphere  itself  (the  equator  and  the  hour-circles)  and  are  not 
affected  at  all  by  the  observer's  journeys,  but  are  as  fixed  as 
the  poles  and  meridians  upon  the  earth ;  the  stars  also,  to  all 
ordinary  observation,  are  fixed  upon  the  sphere  just  as  cities 
are  upon  the  earth.  They  really  move,  of  course,  and  swiftly, 
as  has  been  said  before,  but  they  are  so  far  away  that  it  takes 
centuries,  as  a  rule,  to  produce  the  slightest  apparent  change 
of  place. 

20.  Celestial  Latitude  and  Longitude.  —  A  different  way  of  desig- 
nating the  positions  of  the  heavenly  bodies  in  the  sky  has  come  down 
to  us  from  very  ancient  times.     Instead  of  the  equator  it  makes  use 
of   another  circle  of  reference  in  the  sky,  known  as  the    'Ecliptic' 
This  is  simply  the  apparent  path  described  by  the  sun  in  its  annual 
motion  among  the  stars ;  for  the  sun  appears  to  creep  around  the 


16  CELESTIAL  LATITUDE  AND  LONGITUDE.  t§  2d 

celestial  sphere  in  a  circle  once  every  year,  and  the  Ecliptic  may  be 
defined  as  the  intersection  of  the  plane  of  the  earth's  orbit  with  the 
celestial  sphere,  just  as  the  celestial  equator  is  the  intersection  of  the 
earth's  equator;  the  vernal  equinox  is  one  of  the  points  where  the  two 
circles  cross.  Before  the  days  of  clocks,  the  Ecliptic  was  in  many 
respects  a  more  convenient  circle  of  reference  than  the  equator  and 
was  almost  universally  used  as  such  by  the  old  astronomers.  Celestial 
longitude  and  latitude  are  measured  with  reference  to  the  Ecliptic,  in 
the  same  way  that  right  ascension  and  declination  are  measured  with 
respect  to  the  equator.  Too  much  care  can  hardly  be  taken  to  avoid 
confusion  between  terrestrial  latitude  and  longitude  and  the  celestial 
quantities  that  bear  the  same  name. 


URANOGRAPHY. 


17 


CHAPTER   II 


UKANOGRAPHY. 


GLOBES  AND    STAR-MAPS.  —  STAR    MAGNITUDES.  —  DESIG- 
NATION OF  THE   STARS.  —  THE   CONSTELLATIONS. 

NOTE.  —  It  is  hardly  necessary  to  say  that  this  chapter  is  to  be  treated 
by  the  teacher  differently  from  the  rest  of  the  book.  It  is  to  be  dealt 
with,  not  as  recitation  matter,  but  as  field-work :  to  be  taken  up  at  differ- 
ent times  during  the  course  as  the  constellations  make  their  appearance 
in  the  evening  sky. 

For  convenience  of  reference  we  add  the  following  alphabetical  list  of 
the  constellations  described  or  mentioned  in  the  chapter :  — 


Andromeda 
Anser,  see  Vulpecula  . 

ARTICLE 
.     35 
.     69 

Cepheus 
Cetus  . 

ARTICLE 
.     29 
.     39 

Antinoiis,  see  Aquila  . 
Antlia 
Aquarius     . 

.71 

.    62 

.     78 

Coma  Berenices 
Columba     . 
Corona  Borealis  . 

.    57 
.45 
.    60 

Aquila        . 

71 

Corvus 

.        .        .55 

Argo  Navis 
Aries  .        .        . 

.    51 

38 

Crater 

Cvsnus 

.     55 

.    68 

Auriga        . 
Bootes 
Camelopardus    . 
Cancer 
Canes  Venatici  . 

.    41 

.    59 
.    31 
.     52 
.     58 

Delphmus  . 
Draco. 
Equiileus     . 
Eridanus     . 

.     74 
.        .        .30 
.     75 
.        .    44 
...    47 

Canis  Major 
Canis  Minor 
Capricornus 

.        .49 
.    48 
.73 

Grus    . 
Hercules     . 
Hydra 

.    79 
.    66 
.    55 

Cassiopeia  . 

28 

Lacerta 

.    76 

Centaurus  . 

.    62 

Leo 

.    63 

18 


GLOBES    AND   STAR-MAPS. 


[§21 


Leo  Minor  . 

Lepus 

Libra  . 

Lupus 

Lynx  . 

Lyra   . 

Monoceros  . 

Norma 

Ophiuchus  . 

Orion  . 

Pegasus      . 

Perseus 

Phoanix 

Pisces 

Piscis  Australis  . 


ARTICLE 

.  54 

.  45 

.  61 

.  62 

.  46 

.  67 

.  50 

.  64 

.  65 

.  43 

.  77 

.  40 

.  39 

.  36 

,  79 


A  UTICLE 

(Pleiades) 42 

Sagitta 70 

Sagittarius 72 

Scorpio 63 

Sculptor      .  .        .        .39 

Serpens 65 

Serpentarius,  see  Ophiuchus       .     65 

Sextans 54 

Taurus 42 

Taurus  Poniatovii  .  .  .65 
Triangulum  .  .  .  .37 
Ursa  Major  .  .  .  .26 
Ursa  Minor  .  .  .  .27 

Virgo 56 

Vulp6cula 69 


21.  Globes  and  Star-Maps.  —  In  order  to  study  the  constel- 
lations conveniently,  it  is  necessary  to  have  either  a  celestial 
globe  or  a  star-map,  by  which  to  identify  the  stars.    The  globe 
is  better  and  more  accurate,  if  of  sufficient  size ;  but  is  costly 
and  rather  inconvenient.     (For  a  figure  and  description  of  the 
globe,  see  Appendix,  Art.  400.)    For  most  purposes  a  star-map 
will  answer  just  as  well  as  the  globe,  but  it  can  never  repre- 
sent any  considerable  portion   of  the   sky  correctly  without 
more  or  less  distortion  of  all  the  lines  and  figures  near  the 
margin  of  the  map.     Such  maps  are  made  on  various  systems, 
each  presenting  its   own   advantages.     In   all   of   them   the 
heavens  are  represented  as  seen  from  the  inside,  and  not  as  on 
the  globe,  which  represents  the  sky  as  seen  from  the  outside. 

22.  Star-Maps  of  this  Book.  —  We  present  a  series  of  four 
small  maps,  which,  though  hardly  on  a  large  enough  scale  to 
answer  every  purpose  of  a  complete  celestial  atlas,  are  quite 
sufficient  to  enable  the  student  to  trace  out  the  constellations, 
and  to  identify  the  principal  stars.     In  the  map  of  the  north 
circumpolar  regions,  Map  I.,  the  pole  is  in  the  centre,  and  at 
the  circumference  are  numbered  the  twenty-four  right  ascension 


§  22]  STAR  MAGNITUDES.  19 

hours.  The  parallels  of  declination  are  represented  by  equi- 
distant concentric  circles.  On  the  three  other  rectangular 
maps,  which  show  the  equatorial  belt  of  the  heavens  lying 
between  50°  north  and  50°  south  of  the  equator,  the  parallels 
of  declination  are  horizontal  lines,  while  the  hour-circles  are 
represented  by  vertical  lines,  also  equidistant,  but  spaced  at 
a  distance  which  is  correct,  not  at  the  equator  but  for  declina- 
tion 35°.  This  keeps  the  distortion  within  reasonable  bounds, 
even  near  the  margin  of  the  map,  and  makes  it  very  easy  to 
lay  off  the  places  of  any  object  for  which  the  right  ascension 
and  declination  are  given.  The  ecliptic  is  the  curved  line 
which  extends  across  the  middle  of  the  map.  The  top  of  the 
map  is  north ;  and  the  east,  instead  of  being  at  the  right  hand, 
as  in  a  map  of  the  earth's  surface,  is  to  the  left,  so  that  if  the 
observer  faces  the  south,  and  holds  the  map  up  before  and 
above  him,  the  constellations  which  are  near  the  meridian  will 
be  pretty  truly  represented. 

The  hours  of  right  ascension  are  indicated  on  the  central  horizontal 
line,  which  is  the  celestial  equator,  and  at  the  top  of  the  map  are  given 
the  names  of  the  months.  The  word  "  September,"  for  instance,  means 
that  the  stars  which  are  directly  under  it  on  the  map  will  be  near  the 
meridian  about  9  o'clock  in  the  evening  during  that  month. 

23.  Star  Magnitudes.  —  To  the  eye  the  principal  difference 
in  the  appearance  of  the  different  stars  is  in  their  brightness, 
or  their  so-called  '  magnitude/  Hipparchus  (B.C.  125)  and 
Ptolemy  divided  the  visible  stars  into  six  classes,  the  brightest 
fifteen  or  twenty  being  called  first-magnitude  stars,  and  the 
faintest  which  can  be  seen  by  the  naked  eye  being  called 
sixth. 

It  has  since  been  found  that  the  light  of  the  average  first-magnitude 
star  is  just  about  100  times  as  great  as  that  of  the  sixth ;  and  at  this 
rate,  the  light  of  a  first-magnitude  star  is  just  a  trifle  more  than  equal 
to  two  and  a  half  second-magnitude  stars,  and  a  second-magnitude 
star  to  two  and  a  half  third-magnitude  stars,  etc. 


20  DESIGNATION    OF   THE   STABS.  [§  23 

Our  maps  show  all  the  stars  down  to  about  4£  magnitude, 
about  a  thousand  in  number,  and  all  which  can  be  seen  in  a 
moonlight  night.  A  few  smaller  stars  are  also  inserted  where 
they  mark  some  particular  configuration  or  point  out  some 
interesting  telescopic  object.  Such  double  stars  as  can  be  ob- 
served by  a  three  or  four  inch  telescope  are  marked  on  the  map 
by  underscoring :  two  underscoring  lines  denote  a  triple  star, 
and  three  a  multiple.  A  variable  star  is  denoted  by  a  circle 
enclosing  the  star  symbol.  A  few  clusters  and  nebulae  are  also 
indicated.  The  letter  M.  against  one  of  these  stands  for  '  Mes- 
sier/ who  made  the  first  catalogue  of  103  such  objects  in  1784; 
e.g.,  97  M.  designates  No.  97  on  Messier's  list. 

For  reference  purposes  and  for  study  of  the  heavens  in  detail,  the 
more  elaborate  star-atlases  of  Proctor,  Heis,  or  Klein  are  recommended, 
especially  the  latter,  which  contains  a  great  amount  of  useful  infor- 
mation in  addition  to  the  maps,  and  is  very  cheap  compared  with  the 
others.  The  student  or  teacher  who  possesses  a  telescope  will  also  find 
an  invaluable  accessory  to  it  in  Webb's  "  Celestial  Objects  for  Common 
Telescopes." 

24.  Designation  of  the  Stars.  —  A  few  of  the  brighter  stars 
are  designated  by  names  of  their  own,  and  upon  the  map  those 
names  which  are  in  most  common  use  are  indicated.  Generally, 
however,  the  designation  of  visible  stars  is  by  the  letters  of 
the  Greek  alphabet,  on  a  plan  proposed  in  1603  by  Bayer,  and 
ever  since  followed.  The  letters  are  ordinarily  applied  nearly 
in  the  order  of  brightness,  Alpha  being  the  brightest  star  in 
the  constellation  and  Beta  the  next  brightest ;  but  they  are 
sometimes  applied  to  the  stars  in  their  order  of  position  rather 
than  in  that  of  brightness.  When  the  stars  of  a  constellation 
are  so  numerous  as  to  exhaust  the  letters  of  the  Greek  alpha- 
bet, the  Roman  letters  are  next  used,  —  and  then,  if  necessary, 
we  employ  the  numbers  which  Flamsteed  assigned  a  century 
later.  At  present  every  star  visible  to  the  naked  eye  can  be 
referred  to  and  identified  by  its  number  or  letter  in  the  con- 


§  24]  URSA    MAJOR.  21 

stellation  to  which  it  belongs.     For  the  Greek  Alphabet,  see 
page  344  (Appendix). 

25.  We  begin  our  study  of  Uranography  with  the  constel- 
lations which  are  circumpolar  (i.e.,  within  40°  of  the  north 
pole),  because  these  are  always  visible  in  the  United  States 
and  so  can  be  depended  on  to  furnish  land  (or  rather  sky} 
marks  to  aid  in  tracing  out  the  others.     Since  in  the  latitude 
of  New  York  the  elevation  of  the  pole  is  about  41°,  it  follows 
that  there  (and  this  is  nearly  enough  true  of  the  rest  of  the 
United  States)  all  the  constellations  which  are  within  41°  of 
the  north  pole  will  move  around  it  once  in  twenty-four  hours 
without  setting.     For  this  reason  they  are  called  circumpolar. 
Map  I.  contains  them  all, 

26.  Ursa  Major,  the  Great  Bear  (Map  I.).  —  Of  these  circum- 
polar constellations  none  is  more  easily  recognized  than  Ursa 
Major.     Assuming  the  time  of  observation  as  about  8  o'clock 
in  the  evening  on  Sept.  22d,  it  will  be  found  below  the  pole 
and  to  the  west.     Hold  the  map  so  that  VIII.  is  at  the  bottom 
and  it  will  be  rightly  placed  for  the  time  assumed. 

The  familiar  Dipper  is  sloping  downward  in  the  northwest, 
composed  of  seven  stars,  all  of  about  the  second  magnitude, 
excepting  Delta  (at  the  junction  of  the  handle  to  the  bowl), 
which  is  of  the  third  magnitude.  The  stars  Alpha  (Dubhe), 
and  Beta  (Merati),  are  known  as  the  "Pointers,"  because  a 
line  drawn  from  Beta  through  Alpha  and  produced  about  30° 
passes  very  near  the  Pole-star.  The  dimensions  of  the  Dipper 
furnish  a  convenient  scale  of  angular  measure.  From  Alpha 
to  Beta  is  5° ;  from  Alpha  to  Delta  is  10°  ;  and  from  Alpha  to 
Eta,  at  the  extremity  of  the  Dipper-handle,  (which  is  also  the 
Bear's  tail,)  is  26°.  The  Dipper  (known  also  in  England  as 
the  "  Plough  "  and  as  the  "  Wain,"  or  wagon)  comprises  but  a 
small  part  of  the  whole  constellation.  The  head  of  the  Bear, 
indicated  by  a  small  group  of  scattered  stars,  is  nearly  on  the 


22  URSA  MAJOR.  [§  26 

line  from  Delta  through  Alpha,  carried  on  about  15° ;  at  the 
time  assumed  (Sept.  22d,  8  o'clock)  it  is  almost  exactly  under 
the  pole. 

Three  of  the  four  paws  of  the  creature  are  marked  each  by 
a  pair  of  third  or  fourth  magnitude  stars  1^°  or  2°  apart.  The 
three  pairs  are  nearly  equidistant,  about  20°  apart,  and  almost 
on  a  straight  line  parallel  to  the  diagonal  of  the  Dipper-bowl 
from  Alpha  to  Gamma,  but  some  20°  south  of  it.  At  the  time 
assumed  they  are  all  three  very  near  the  horizon  for  an  ob- 
server in  latitude  40°,  but  during  the  spring  or  summer,  when 
the  constellation  is  high  in  the  sky,  they  can  be  easily  made 
out. 

The  star  Zeta  (or  Mizar),  at  the  bend  in  the  handle,  is 
easily  recognized  by  the  little  star  Alcor  near  it.  Mizar  it- 
self is  a  double  star,  easily  seen  as  double  with  a  small  tel- 
escope, and  one  of  the  most  interesting  recent  astronomical 
results  is  the  discovery  that  it  is  really  triple,  the  larger  of 
the  two  stars  being  itself  double,  invisibly  so  to  the  telescope, 
but  revealing  its  double  character  by  means  of  the  lines  in 
its  spectrum  (see  Art.  373).  The  star  Xi,  the  southern  one  of 
the  pair,  which  marks  the  left-hand  paw,  is  also  double  and 
binary,  i.e.,  the  two  stars  which  compose  it  revolve  about  their 
common  centre  of  gravity  in  about  sixty-one  years.  (For 
diagram  of  the  orbit,  see  Fig.  77,  Art.  369.)  It  was  the  first 
binary  whose  orbit  was  computed. 

According  to  the  ancient  legends,  Ursa  Major  is  Callisto,  the  daugh- 
ter of  Lycaon,  king  of  Arcadia.  The  jealousy  of  Juno  l  changed  her 
into  a  bear,  and  afterwards  Jupiter  placed  her  among  the  constella- 
tions with  Areas  her  son,  who  became  Ursa  Minor.  One  of  the  quaint 

1  We  have  followed  throughout  the  Roman  nomenclature  of  the  gods 
and  heroes,  as  used  by  Virgil  and  Ovid ;  but  the  reader  should  be  reminded 
that,  in  many  important  respects,  these  Roman  personages  differ  from 
the  Greek  divinities  who  were  identified  with  them.  It  should  be  said, 
also,  that  in  many  cases  the  old  legends  are  greatly  confused  and  often 
contradictory,  as,  for  instance,  in  the  case  of  Hercules. 


§27]  URSA   MINOR.  23 

old  authors  explains  the  very  un-bearlike  length  of  the  creatures'  tails, 
by  saying  that  they  stretched  as  Jupiter  lifted  them  to  the  sky. 

27.  Ursa  Minor,  the  Lesser  Bear  (Map  I.).  —  The  line  of  the 
"Pointers"  unmistakably  marks  out  the  Pole-star  (Polaris), 
a  star  of  the  second  magnitude,  standing  quite  alone.  It  is 
at  the  end  of  the  tail  of  Ursa  Minor,  or  at  the  extremity  of 
the  handle  of  the  "  Little  Dipper " ;  for  in  Ursa  Minor,  also, 
the  seven  principal  stars  form  a  dipper,  though  with  the  handle 
bent  in  a  different  way  from  that  of  the  other  dipper.  Begin- 
ning at  Polaris,  a  curved  line  (concave  towards  Ursa  Major) 
drawn  through  Delta  and  Epsilon  brings  us  to  Zeta,  where  the 
handle  joins  the  bowl.  Two  bright  stars  (second  and  third 
magnitude),  Beta  and  Gamma,  correspond  to  the  Pointers  in 
the  large  Dipper,  and  are  known  as  the  "  Guardians  of  the 
Pole  "  ;  Beta  is  named  Kochab.  The  pole  now  lies  about  1J° 
from  the  Pole-star,  on  the  line  joining  it  to  Mizar  (at  the 
bend  in  the  handle  of  the  large  Dipper). 

It  has  not  always  been  so.  Some  4000  years  ago  the  star  Thuban 
(Alpha  Draconis)  was  the  Pole-star,  and  2000  years  ago  the  present 
Pole-star  was  very  much  farther  from  the  pole  than  now.  At  present 
the  pole  is  coming  nearer  to  the  star,  and  towards  the  close  of  the 
next  century  it  will  be  within  half  a  degree  of  it.  Twelve  thousand 
years  hence  the  bright  star  Alpha  Lyrse  will  be  the  Pole-star,  —  and 
this  not  because  the  stars  change  their  positions,  but  because  the  axis 
of  the  earth  slowly  changes  its  direction,  owing  to  'precession '  (see 
Art.  125). 

The  Greek  name  of  the  Pole-star  was  Cynosura,  which 
means  the  '  tail  of  the  Dog,'  indicating  that  at  one  time  the 
constellation  was  understood  to  represent  a  Dog  instead  of  a 
Bear. 

As  already  said  (Art.  26)  this  constellation  is  by  many  writers 
identified  with  Areas,  Callisto's  son.  But  more  generally  Areas  is 
identified  with  Bootes. 

The  Pole-star  is  double,  having  a  small  companion  barely 
visible  with  a  telescope  of  two  or  three  inches  diameter. 


24  CASSIOPEIA.  [§  28 

28.  Cassiopeia  (Map  I.).  —  This  constellation  lies  on  the  op- 
posite side  of  the  pole  from  the  Dipper,  and  at  about  the  same 
distance  from  it  as  the  "  Pointers."  It  is  easily  recognized  by 
the  zigzag,  "  rail-fence  "  configuration  of  the  five  or  six  bright 
stars  that  mark  it.  With  the  help  of  the  rather  inconspicuous 
star  Kappa,  one  can  make  out  of  them  a  pretty  good  chair  with 
the  feet  turned  away  from  the  pole.  But  this  is  wrong.  In  the 
recognized  figures  of  the  constellation  the  lady  sits  with  feet 
towards  the  pole,  and  the  bright  star  Alpha  is  in  her  bosom, 
while  Zeta  and  the  other  faint  stars  north  of  Alpha  are  in  her 
head  and  uplifted  arms ;  Iota,  on  the  line  from  Delta  to  Epsilon 
produced,  is  in  the  foot.  The  order  of  the  principal  stars  is 
easily  remembered  by  the  word  'Bagdei,'  i.e.,  Beta,  Alpha, 
Gamma,  Delta,  Epsilon,  Iota. 

Alpha,  which  is  slightly  variable  in  brightness,  is  known  as 
Schedir  ;  Beta  is  called  Caph.  The  little  star  Eta,  which  is 
about  half-way  between  Alpha  and  Gamma,  a  little  off  the 
line,  is  a  very  pretty  double  star,  —  the  larger  star  orange,  the 
smaller  one  purple.  It  is  binary  (i.e.,  the  two  stars  revolve 
around  each  other),  with  a  period  of  about  206  years. 

In  the  year  1572  a  famous  temporary  star  made  its  appear- 
ance in  this  constellation,  at  a  point  on  the  line  drawn  from 
Gamma  through  Kappa,  and  extended  about  half  its  length. 
It  was  carefully  observed  and  described  by  Tycho  Brahe,  and 
at  one  time  was  bright  enough  to  be  seen  easily  in  broad  day- 
light. There  has  been  an  entirely  unfounded  notion  that  this 
was  identical  with  the  Star  of  Bethlehem,  and  there  has  been 
an  equally  unfounded  impression  that  its  reappearance  may  be 
expected  about  the  present  time. 

Cassiopeia  was  the  wife  of  Cepheus,  king  of  Libya,  and  the  mother 
of  Andromeda,  who  was  rescued  from  the  sea-monster,  Cetus,  by  Per- 
seus, who  came  flying  through  the  air,  and  used  the  head  of  Medusa, 
(which  he  still  holds  in  his  hand,)  to  turn  his  adversaries  to  stone. 
Cassiopeia  had  indulged  in  too  great  boasting  of  her  daughter's  beauty, 


§  29]  CEPHEUS  —  DRACO.  25 

and  thus  excited  the  jealousy  of  the  Nereids,  at  whose  instigation  the 
sea-monster  was  sent  by  Neptune  to  ravage  the  kingdom. 

29.  Cepheus  (Map  I.).  —  This  constellation,  though  large, 
contains   very  few  bright   stars.     At  the   assumed  time  (8 
o'clock,  Sept.  22d)  it  is  above  Cassiopeia  and  to  the  west,  not 
having  quite  reached  the  meridian  above  the  pole.     A  line 
carried  from  Alpha  Cassiopeia  through  Beta,  and  produced  20°, 
will  pass  very  near  to  Alpha  Cephei,  a  star   of  the   third 
magnitude  in  the  king's  right  shoulder.    Beta  Cephei  is  about 
8°  north  of  Alpha,  and  Gamma  about  12°  from  Beta,  both  also 
of  the  third  magnitude.     Gamma  is  so  placed  that  it  is  at  the 
obtuse  angle  of  a  rather  flat  isosceles  triangle  of  which  Beta 
Cephei  and  the  Pole-star  form  the  other  two  corners.    Cepheus 
is  represented  as  sitting  behind  Cassiopeia  (his  wife)  with  his 
feet  upon  the  tail  of  the  Little  Bear,  Gamma  being  in  his  left 
knee.     His   head  is   marked   by  a  little   triangle  of  fourth- 
magnitude  stars,  of  which  Delta  is  a  remarkable  variable  with 
a  period  of  5J  days.     It  is  worth  noting  that  there  are  several 
other  small  variable  stars  in  the  same  neighborhood  (none  of 
them  bright  enough  to  be  shown  upon  the  map).     Beta  is  a 
very  pretty  double  star. 

30.  Draco,  the  Dragon  (Map  I.).  —  The   constellation  of 
Draco  is  characterized  by  a  long,  winding  line  of  stars,  mostly 
small,  extending  half-way  around  the  pole  and  separating  the 
two  Bears.     A  line  from  Delta  Cassiopeia  drawn  through  Beta 
Cephei  and  extended  about  as  far  again  will  fall  upon  the  head 
of  Draco,  marked  by  an  irregular  quadrilateral  of  stars,  two 
of  which  are  of  the  2^  and  3  magnitude.     These  two  bright 
stars  about  4°  apart  are  Beta  and  Gamma.     The  latter  (named 
Etaniri),  in  its  daily  revolution,  passes  almost  exactly  through 
the  zenith  of  Greenwich,  and  it  was  by  observations  upon  it 
that  the  "aberration  of  light"  was  discovered  (see  Art.  435). 
The  nose  of  Draco  is  marked  by  a  smaller   star,  Mu,  some 
5°  beyond  Beta,  nearly  on  the  line   drawn  through  it  from 


26  DKACO.  [§  30 

Gamma.  From  Gamma  we  trace  the  neck  of  Draco,  eastward 
and  downward *  toward  the  Pole-star,  until  we  come  to  Delta 
and  Epsilon  and  some  smaller  stars  near  them. 

There  the  direction  of  the  line  is  reversed,  as  shown  upon  the 
map,  so  that  the  body  of  the  monster  lies  between  its  own  head 
and  the  bowl  of  the  Little  Dipper,  and  winds  around  this  bowl 
until  the  tip  of  the  tail  is  reached,  at  the  middle  of  the  line 
between  the  Pointers  and  the  Pole-star.  The  constellation 
covers  more  than  12  hours  of  right  ascension. 

One  star  deserves  special  notice,  the  star  Alpha  or  Thuban, 
a  star  of  3J  magnitude,  which  lies  half-way  between  Zeta  Ursee 
Majoris  (Mizar)  and  Gamma  Ursa  Minoris.  Four  thousand 
seven  hundred  years  ago  it  was  the  Pole-star,  and  then  within 
a  quarter  of  a  degree  of  the  pole,  much  nearer  than  Polaris  is 
at  present  or  ever  will  be.  It  is  probable  also  that  its  bright- 
ness has  considerably  fallen  off  within  the  last  200  years,  since 
among  the  ancient  astronomers  it  was  always  reckoned  as  of 
the  second  magnitude  and  is  not  now  much  above  the  fourth. 
The  so-called  'Pole  of  the  Ecliptic '  is  in  this  constellation, 
i.e.,  the  point  which  is  90°  distant  from  every  point  in  the 
Ecliptic,  the  circle  annually  described  by  the  sun.  This  point 
(see  map)  is  the  centre  around  which  precession  causes  the 
pole  to  move  nearly  in  a  circle  (see  Art.  126)  once  in  25,800 
years. 

The  mythology  of  this  constellation  is  doubtful.  According  to 
some  it  is  the  dragon  which  Cadmus  slew,  afterwards  sowing  its  teeth, 
from  which  sprung  up  the  harvest  of  armed  men  who  fought  and  slew 
each  other,  leaving  only  the  five  survivors  who  were  the  founders  of 
Thebes.  Others  say  that  it  was  the  dragon  who  watched  the  golden 
apples  of  the  Hesperides,  and  was  killed  by  Hercules  when  he  cap- 
tured that  prize.  This  accords  best  with  the  fact  that  in  the  heavens 
Hercules  has  his  foot  on  the  dragon's  head. 


1  The  description  applies  strictly  only  at  the  time  assumed,  8  o'clock, 
Sept.  22d. 


§  31]  THE   MILKY   WAY.  27 

31.  Camelopardus.  —  This  is  the  only  remaining  one  of  the  strictly 
circumpolar  constellations,  —  a  modern  one  containing  no  stars  above 
fourth  magnitude,  and  established  by  Hevelius  (1611-1687)  simply  to 
cover  the  great  empty  space  between  Cassiopeia  and  Perseus  on  one 
side,  and  Ursa  Major  and  Draco  on  the  other.     The  animal  stands  on 
the  head  and  shoulders  of  Auriga,  and  his  head  is  between  the  Pole- 
star  and  the  tip  of  the  tail  of  Draco. 

The  two  constellations  of  Perseus  (which  at  the  time  assumed  is 
some  20°  below  Cassiopeia),  and  of  Auriga,  are  partly  circumpolar,  but 
on  the  whole  can  be  more  conveniently  treated  in  connection  with  the 
equatorial  maps.  Capella,  the  brightest  star  of  Auriga,  and  next  to 
Vega  and  Arcturus  the  brightest  star  in  the  northern  hemisphere, 
is  at  the  time  assumed  (Sept.  22d,  8  o'clock)  a  few  degrees  above 
the  horizon  in  the  N.E.  Between  it  and  the  nose  of  Ursa  Major  lies 
part  of  the  constellation  of  the  Lynx,  a  modern  one,  made,  like 
Camelopardus,  by  Hevelius,  merely  to  fill  a  gap,  and  without  any 
large  stars. 

32.  The  Milky  Way  in  the  Circumpolar  Region.  —  The  only 
circumpolar  constellations  traversed  by  the  Milky  Way  are 
Cassiopeia  and  Cepheus.    It  enters  the  circumpolar  region  from 
the  constellation  of  Cygnus,  which  at  this  time  is  just  in  the 
zenith,  sweeps  down  across  the  head  and  shoulders  of  Cepheus, 
and  on  through  Cassiopeia  and  Perseus  to  the  northeastern 
horizon  in  Auriga.     There  is  one  very  bright  patch  a  few 
degrees  north  of  Beta  Cassiopeise,  and  half  way  between  Delta 
Cassiopeiae  and  Gamma  Persei  there  is  another  bright  cloud 
in  which  is  the  famous  double  cluster  of  the  "  Sword-handle 
of  Perseus," — a  beautiful  object  for  even  the  smallest  tele- 
scope. 

33.  For  the  most  part  the  constellations  shown  upon  the 
circumpolar  map  (I.)  will  be  visible  every  night  in  the  north- 
ern part  of  the  United  States.    At  places  farther  south  the  con- 
stellations near  the  rim  of  the  map  will  stay  below  the  horizon 
for  a  short  time  every  twenty-four  hours,  since  the  height  of 
the  pole  always  equals  the  latitude  of  the  observer,  and  there- 
fore only  those  stars  which  have  a  polar  distance  less  than  the 


28  TIMES   FOR  OBSERVATION  [§  33 

latitude  will  remain  constantly  visible.  In  other  words,  if, 
with,  the  pole  as  a  centre,  we  draw  a  circle  with  a  radius  equal 
to  the  height  of  the  pole  above  the  horizon,  all  the  stars  within 
this  circle  will  remain  continually  above  the  horizon.  This  is 
called  the  circle  of  '  Perpetual  Apparition.7  (Art.  85.)  At 
New  Orleans,  in  latitude  30°,  its  radius,  therefore,  is  only  30°, 
and  only  those  stars  which  are  within  30°  of  the  pole  will 
make  a  complete  circle  without  setting.  At  stations  in  the 
northern  part  of  the  United  States,  as  Tacoma,  it  is  nearly  as 
large  as  the  whole  map. 

34.  Before  proceeding  to  consider  the  other  constellations, 
the  student  should  be  reminded  that  he  will  have  to  select 
those   that  are   conveniently  visible  at  the  time  of  the  year 
when  he  happens  to  be  studying  the  subject,  and  that,  if  he 
wishes  to  cover  the  whole  sky,  he  will  have  to  take  up  the  sub- 
ject more  than  once,  and  at  various  seasons  of  the  year.     The 
constellations  near  the  southern  limits  of  the  map  especially 
can  be  seen  only  a  few  weeks  in  each  year. 

He  will  also  be  likely  to  be  occasionally  perplexed  by  find- 
ing in  the  heavens  certain  conspicuous  stars  not  given  on  the 
maps,  —  stars  much  brighter  than  any  that  are  given.  These 
are  the  planets  Venus,  Jupiter,  Mars,  and  Saturn,  called  planets, 
i.e.,  '  wandering  stars,'  just  because  they  continually  change 
their  place,  and  so  cannot  be  mapped.  The  student  will  find 
it  interesting  and  instructive,  however,  to  dot  down  upon  the 
star-map  every  clear  night  the  places  of  any  planets  he  may 
notice,  and  thus  to  follow  their  motion  for  a  month  or  two. 

Remember  also  that  on  these  maps  east  always  lies  on  the 
left  hand,  so  that  the  map  should  be  held  between  the  eye  and 
the  sky  in  order  to  represent  things  correctly.  We  begin  with 
Andromeda  at  the  N.W.  corner  of  Map  II. 

35.  Andromeda  (Map  II.).     November.  —  Andromeda  will 
be  found  exactly  overhead  in  our  latitudes  about  9  o'clock  in 


§  35]  ANDROMEDA  —  PISCES.  29 

the  middle  of  November.  Its  characteristic  configuration  is  the 
line  of  three  second-magnitude  stars,  Alpha,  Beta,  and  Gamma, 
extending  east  and  north  from  Alpha,  (Alpheratz)  which 
itself  forms  the  N.E.  corner  of  the  so-called  "Great  Square 
of  Pegasus,"  and  is  sometimes  lettered  as  Delta  Pegasi.  This 
star  may  readily  be  found  by  extending  an  imaginary  line  from 
Polaris  through  Beta  Cassiopeise,  and  producing  it  about  as 
far  again :  Alpha  is  in  the  head  of  Andromeda,  Beta  (MiracJi) 
in  her  waist,  and  Gamma  (Almaach)  in  her  left  foot.  A  line 
drawn  northwesterly  from  Beta,  nearly  at  right  angles  to 
the  line  Beta  Gamma,  will  pass  through  Mu  at  a  distance  of 
about  5°,  and  produced  another  5°  will  strike  the  "great 
nebula,"  which  is  visible  to  the  naked  eye  like  a  little  cloud  of 
light,  and  forms  a  small  obtuse-angled  triangle  with  Nu  and 
a  little  sixth-magnitude  star.  Andromeda  has  her  mother, 
Cassiopeia,  close  by  on  the  north,  with  her  father,  Cepheus, 
not  far  away,  while  at  her  feet  is  Perseus,  her  deliverer.  Her 
head  rests  upon  the  shoulder  of  Pegasus.  In  the  south, 
beyond  the  constellations  of  Aries  and  Pisces,  Cetus,  the  sea- 
monster,  who  was  to  have  devoured  her,  stretches  his  ungainly 
bulk. 

We  have  already  mentioned  the  nebula.  Another  very  pretty 
object  is  Gamma,  which  in  a  small  instrument  is  a  double  star,  the 
larger  one  orange,  the  smaller  a  greenish  blue.  The  small  star  is  itself 
double,  making  the  system  really  triple,  but  as  such  is  beyond  the 
reach  of  any  but  very  large  instruments. 

When  Neptune  sent  the  leviathan,  Cetus,  to  ravage  Libya,  the  ora- 
cle of  Ammon  announced  that  the  kingdom  could  be  delivered  only 
if  Cepheus  would  give  up  his  daughter.  He  assented  and  chained  the 
poor  girl  to  a  rock  to  await  her  destruction.  But  Perseus,  returning 
through  the  air  from  the  slaying  of  the  Gorgon,  Medusa,  saw  her, 
rescued  her,  won  her  love,  and  made  her  his  wife. 

36.  Pisces,  the  Fishes  (Map  II.).  November. — Immediately 
south  of  Andromeda  lies  Pisces,  the  first  of  the  constellations 


30  TRIANGTJLUM.  [§  36 

of  the  Zodiac,1  which  is  a  belt  16°  wide  (8°  on  each  side  of 
the  ecliptic)  encircling  the  heavens,  and  including  the  space 
within  the  limits  of  which  the  sun,  the  moon,  and  all  the  prin- 
cipal planets  perform  their  apparent  motions.  At  present,  in 
consequence  of  precession,  it  occupies  the  sign  of  Aries  (see 
Art.  126).  It  has  not  a  single  conspicuous  star,  and  is  notable 
only  as  now  containing  the  Vernal  Equinox,  or  "First  of 
Aries,"  which  lies  near  the  southern  boundary  of  the  constel- 
lation in  a  peculiarly  starless  region.  A  line  from  Alpha  An- 
dromedse  through  Gamma  Pegasi,  continued  as  far  again,  strikes 
about  2°  east  of  the  point.  The  body  of  one  of  the  two  fishes 
lies  about  15°  south  of  the  middle  of  the  southern  side  of  the 
"Great  Square  of  Pegasus/'  and  is  marked  by  an  irregular 
polygon  of  small  stars,  5°  or  6°  in  diameter.  A  long,  crooked 
"ribbon"  of  little  stars  runs  eastward  for  more  than  30°, 
terminating  in  Alpha  Piscium,  (called  El  Risclia,  or  'the 
knot,')  a  star  of  the  fourth  magnitude  20°  south  of  the  head 
of  Aries.  From  there  another  line  of  stars  leads  up  north- 
west in  the  direction  of  Delta  Andromedse  to  the  northern 
fish,  which  lies  in  the  vacant  space  south  of  Beta  Andromedse. 

Alpha  is  a  very  pretty  double  star,  the  two  components  being  about 
2"  apart. 

The  mythology  of  this  constellation  is  not  very  well  settled.  One 
story  is  that  the  fishes  are  Venus  and  her  son  Cupid,  who  once  were 
thus  transformed  when  endeavoring  to  escape  from  the  giant  Typhon. 
The  northern  fish  is  Cupid,  the  southern  his  mother. 

37.  Triangulum  or  Deltoton,  the  Triangle  (Map  II.).  De- 
cember. —  This  little  constellation,  insignificant  as  it  is,  is  one 
of  Ptolemy's  ancient  -forty-eight.  It  lies  half-way  between 
Gamma  Andromedse  and  the  head  of  Aries,  and  is  character- 

1  The  word  is  derived  from  the  Greek  word  zoon,  a  living  creature, 
and  indicates  that  all  the  constellations  in  it  (Libra  alone  excepted)  are 
animals.  The  zodiacal  constellations  are  for  the  most  part  of  remote 
antiquity,  antedating  by  many  centuries  even  the  Greek  mythology. 


§  38]  ARIES  —  CETUS.  31 

ized  by  three  stars  of  the  third  and  fourth  magnitude,  easily 
made  out  by  the  help  of  the  map. 

It  may  be  regarded  as  a  canonization  of  "  Divine  Geometry,"  but 
has  no  special  mythological  legend  connected  with  it. 

38.  Aries,  the  Earn  (Map  II).    December. — This  is  the  sec- 
ond of  the  zodiacal  constellations,  now  occupying  the  sign  of 
Taurus.     It  lies  just  south  of  Triangulum  and  Perseus.     Its 
characteristic  star-group  is  that  composed  of  Alpha  (Hamal), 
Beta,  and  Gamma  (see  map),  about  20°  due  south  of  Gamma 
Andromedse.     Alpha,  a  star  of  2^  magnitude,  is  fairly  conspic- 
uous, forming  a  large  isosceles  triangle  with  Beta  and  Gamma 
Andromedse. 

Gamma  Arietis  is  a  very  pretty  double  star  with  the  components 
about  9"  apart.  It  is  probably  the  first  double  star  discovered,  hav- 
ing been  noticed  by  Hooke  in  1664. 

The  star  41  Arietis  (3}  magnitude),  which  forms  a  nearly  equilat- 
eral triangle  with  Alpha  Arietis  and  Gamma  Trianguli,  constitutes, 
with  two  or  three  other  stars  near  it,  the  constellation  of  Musca 
(Borealis),  a  constellation,  however,  not  now  generally  recognized. 

According  to  the  Greeks,  Aries  is  the  ram  which  bore  the  golden 
fleece  and  dropped  Helle  into  the  Hellespont,  when  she  and  her  brother, 
Phrixus,  were  flying  on  its  back  to  Colchis.  Long  afterwards  the 
Argonautic  Expedition,  with  Jason  as  its  head  and  Hercules  as  one 
of  its  members,  sailed  from  Greece  to  Colchis  to  recover  the  fleece, 
and  finally  succeeded  after  long  endeavors. 

39.  Cetus,  the  Sea-monster  (Map  II.).     November-Decem- 
ber. —  South  of  Aries  and  Pisces  lies  the  huge  constellation 
of  Cetus,  the  sea-monster,  which  backs  up  into  the  sky  from 
the  southeastern  horizon.     The  head  lies  some  20°  southeast 
of  Alpha  Arietis,  and  is  marked  by  an  irregular  five-sided  fig- 
ure of  stars,  each  side  being  some  5°  or  6°  long.     The  southern 
edge  of  this  pentagon  is  formed  by  the  stars  Alpha  or  Merikar 
(21  magnitude)  and  Gamma  (3J  magnitude)  ;  Delta  lies  south- 
west of  Gamma.     Beta  (Deneb  Ceti),  the  brightest  star  of  the 


32  PERSEUS.  [§  39 

I 

constellation  (2  magnitude),  stands  by  itself  nearly  40°  west 
and  south  of  Alpha.  Gamma  is  a  very  pretty  double  star,  but 
rather  close  for  a  small  telescope,  the  components  being  only 
2.5"  apart,  yellow  and  blue. 

Cetus  is  the  leviathan  that  was  sent  by  Neptune  to  ravage  Libya 
and  devour  Andromeda.  Perseus  turned  him  into  stone  by  showing 
him  the  head  of  the  Gorgon,  Medusa.  On  the  globes  he  is  usually 
represented  as  a  nondescript  sort  of  beast,  with  a  face  like  a  puppy's, 
and  a  tightly  curled  tail;  as  if  the  Gorgon's  head  had  frightened  out 
all  his  savageness. 

South  of  Cetus  lies  the  modern  constellation  of  Sculptoris  Appa- 
ratus (usually  known  simply  as  Sculptor),  which,  however,  contains 
nothing  that  requires  notice  here.  South  of  Sculptor,  and  close  to 
the  horizon,  even  when  on  the  meridian,  is  Phoenix.  It  has  some 
bright  stars,  but  none  easily  observable  in  the  United  States. 

40.  Perseus  (Maps  I.  and  II.).  January.  —  Keturning  now 
to  the  northern  limit  of  the  map,  we  come  to  the  constella- 
tion of  Perseus.  Its  principal  star  is  Alpha  (Algenib),  rather 
brighter  than  the  standard  second  magnitude,  and  situated 
very  nearly  on  the  prolongation  of  the  line  of  the  three  chief 
stars  of  Andromeda.  A  very  characteristic  configuration  is 
the  so-called  "  segment  of  Perseus "  (Map  I.),  a  curved  line 
formed  by  Delta,  Alpha,  Gamma,  and  Eta,  with  some  smaller 
stars,  concave  towards  the  northeast,  and  running  along  the 
line  of  the  Milky  Way  towards  Cassiopeia.  The  remarkable 
variable  star,  Beta,  or  Algol,  is  situated  about  9°  south  and  a 
little  west  of  Alpha,  at  the  right  angle  of  a  right-angled  triangle 
which  it  forms  with  Alpha  Persei  and  Gamma  Andromedse. 
Algol  and  a  few  small  stars  near  it  form  "  Medusa's  Head," 
which  Perseus  carries  in  his  hand.  For  further  particulars 
and  recent  discoveries  regarding  this  star,  see  Arts.  358  and 
360. 

Epsilon  is  a  very  pretty  double  star  with  the  components  about  8" 
apart;  but  the  most  beautiful  telescopic  object  in  the  constellation, 


§  40]  AURIGA.  33 

perhaps  the  finest,  indeed,  in  the  whole  heavens  for  a  small  telescope, 
is  the  pair  of  clusters  about  half-way  between  Gamma  Persei  and 
Delta  Cassiopeiae,  visible  to  the  naked  eye  as  a  bright  knot  in  the 
Milky  Way,  and  already  referred  to  in  Art.  32. 

Perseus  was  the  sen  of  Danae  by  Jupiter,  who  won  her  in  a  shower 
of  gold.  He  was  sent  by  his  enemies  on  the  desperate  venture  of 
capturing  the  head  of  Medusa,  the  only  mortal  one  of  the  three  Gor- 
gons,  which  were  frightful  female  monsters  with  wings,  tremendous 
claws,  and  brazen  teeth,  and  serpents  for  hair ;  of  such  aspect  that  the 
sight  turned  all  who  looked  at  them  to  stone.  The  gods  helped  Per- 
seus by  various  gifts  which  enabled  him  to  approach  his  victim,  invis- 
ible and  unsuspected,  and  to  deal  the  fatal  blow  without  looking  at  the 
sight  himself.  From  the  blood  of  Medusa,  where  her  body  fell,  sprang 
Pegasus,  the  winged  horse,  and  where  the  drops  fell  on  the  sands  of 
Libya,  as  Perseus  was  flying  across  the  desert,  thousands  of  venomous 
serpents  swarmed.  On  his  way,  returning  home,  he  saw  and  rescued 
Andromeda,  as  already  mentioned  (Arts.  28  and  34).  Hercules  was 
one  of  their  descendants. 

41.  Auriga,  the  Charioteer  (Maps  I.  and  II.).  January. — 
Proceeding  east  from  Perseus  we  come  to  Auriga,  who  is 
represented  as  holding  in  his  arms  a  goat  and  her  kids.  The 
constellation  is  instantly  recognized  by  the  bright  yellow  star, 
Capella  (the  Goat),  and  her  attendant  'Hoedi'  (the  Kids). 
Alpha  Aurigse  (Capella)  is,  according  to  Pickering,  precisely 
of  the  same  brightness  as  Vega,  both  of  them  being  about  •£•  of 
a  magnitude  fainter  than  Arcturus,  but  distinctly  brighter 
than  any  other  stars  visible  in  our  latitudes  except  Sirius  itself. 
The  spectroscope  shows  that  Capella  is  very  similar  in  charac- 
ter to  our  own  sun,  though  probably  vastly  larger.  About  10° 
east  of  Capella  is  Beta  Aurigse  (Menkalinan)  of  the  second 
magnitude ;  Epsilon,  Zeta,  and  Eta,  which  form  a  long  triangle 
4°  or  5°  south  of  Alpha,  are  the  Kids. 

There  seems  to  be  no  well-settled  mythological  history  for  this 
constellation,  though  some  say  that  he  is  the  charioteer  of  (Enomaus, 
king  of  Elis;  while  others  connect  him  with  the  story  of  Phaeton, 
the  son  of  Apollo,  who  borrowed  the  horses  of  his  father  and  was  over- 


34  TAURUS.  [§  42 

thrown  in  mid-heaven.  The  goat  is  supposed  to  be  Amalthea,  the  goat 
which  suckled  Jupiter  in  his  infancy.  Capella  and  the  Kids  were  al- 
ways regarded  by  astrologers  as  of  kindly  influence,  especially  towards 
sailors. 

42.  Taurus,  the  Bull  (Map  III.).  January.  —  This,  the 
third  of  the  zodiacal  constellations,  lies  directly  south  of  Per- 
seus and  Auriga,  and  north  of  Orion.  It  is  unmistakably 
characterized  by  the  Pleiades,  and  by  the  V-shaped  group  of 
the  Hyades  which  forms  the  face  of  the  bull,  with  the  red 
Aldebaran  (Alpha  Tauri),  a  standard  first-magnitude  star, 
blazing  in  the  creature's  eye,  as  he  charges  down  upon  Orion. 
His  long  horns  reach  out  towards  Gemini  and  Auriga,  and 
are  tipped  with  the  second  and  third  magnitude  stars,  Beta 
and  Zeta.  As  in  the  case  of  Pegasus,  only  the  head  and 
shoulders  appear  in  the  constellation.  Six  of  the  Pleiades 
are  easily  visible,  and  on  a  dark  night  a  fairly  good  eye  will 
count  nine  of  them.  With  a  three-irich  telescope  about  100 
stars  are  visible  in  the  cluster,  which  is  more  fully  described 
with  a  figure  in  Art.  376.  The  brightest  of  the  Pleiades  is 
called  '  Alcyone?  and  was  assigned  to  the  dignity  of  the 
< Central  Sun'  by  Maedler  (Art.  386). 

About  1°  west  and  a  little  north  of  Zeta  is  a  nebula  (Messier  1), 
which  has  many  times  been  discovered  by  tyros  with  a  small  telescope 
as  a  new  comet :  it  is  an  excellent  imitation  of  the  real  thing. 

According  to  the  Greek  legends,  Taurus  is  the  milk-white  bull  into 
which  Jupiter  changed  himself  when  he  carried  away  Europa  from 
Phoenicia  to  the  island  of  Crete,  where  she  became  the  mother  of 
Minos  and  the  grandmother  of  Deucalion,  the  Noah  of  Greek  my- 
thology. But  Taurus,  like  most  of  the  other  zodiacal  constellations,  is 
really  far  older  than  the  Greek  mythology,  and  appears  in  the  most 
ancient  zodiacs  of  Egypt,  where  it  was  probably  connected  with  the 
worship  of  the  bull,  Apis ;  so  also  in  the  ancient  Astronomy  of  Chal- 
dea  and  India. 

The  Pleiades  were  daughters  of  the  giant  Atlas.  Of  the  seven 
sisters,  one,  who  married  a  mortal,  lost  her  brightness,  according 


§  42]  ORION.  35 

to  the  legend,  so  that  only  six  remain  visible.  Some  say  that  Merope 
was  the  one  who  thus  gave  up  her  immortality  for  love,  but  her  star  is 
still  visible,  while  Celaeno  and  Asterope  are  both  faint.  The  now  rec- 
ognized names  of  the  stars  in  the  group  (see  map,  Art.  376)  include 
Atlas  and  Pleione,  the  parents  of  the  family,  as  well  as  the  seven  sis- 
ters. As  for  the  Hyades,  who  .were  half-sisters  of  the  Pleiades,  there 
is  less  legendary  interest  in  their  case.  They  are  always  called  by 
the  poets  "  the  rainy  Hyades." 

43.  Orion  (not  O'rion)  (Map  II.).  February.  —  This  is  the 
most  splendid  constellation  in  the  heavens.  As  the  giant 
stands  facing  the  bull,  his  shoulders  are  marked  by  the  two 
bright  stars,  Alpha  (Betelgueze)  and  Gamma  (Bellatrix),  the 
former  of  which  in  color  closely  matches  Aldebaran,  though 
its  brightness  is  somewhat  variable.  In  his  left  hand  he  holds 
up  the  lion  skin,  indicated  by  the  curved  line  of  little  stars 
between  Gamma  and  the  Hyades.  The  top  of  the  club,  which 
he  brandishes  in  his  right  hand,  lies  between  Zeta  Tauri  and 
Mu  and  Eta  Geminorum.  His  head  is  marked  by  a  little  tri- 
angle of  stars  of  which  Lambda  is  the  chief.  His  belt,  through 
the  northern  end  of  which  passes  the  celestial  equator,  consists 
of  three  stars  of  the  second  magnitude,  pointing  obliquely 
southeast  toward  Sirius.  It  is  very  nearly  3°  in  length,  and 
is  known  in  England  as  the  "  Ell  and  Yard."  From  the  belt 
hangs  the  sword,  composed  of  three  smaller  stars  lying  more 
nearly  north  and  south :  the  middle  one  of  them  is  the  mul- 
tiple, Theta,  in  the  great  nebula,  which  even  in  a  small  tele- 
scope is  a  beautiful  object,  the  finest  nebula  in  the  sky.  Beta 
Orionis,  or  Rigel,  a  magnificent  white  star,  is  in  the  left  foot, 
and  Kappa  is  in  the  right  knee.  Orion  has  no  right  foot,  or  if 
he  has,  it  is  hidden  behind  Lepus.  The  quadrilateral  Alpha, 
Gamma,  Beta,  Kappa,  with  the  diagonal  belt,  Delta,  Eta,  Zeta, 
once  learned  can  never  be  mistaken  for  anything  else  in  the 
heavens. 

Rigel  is  a  very  pretty  double  star,  the  larger  star  having  a  very 
small  companion  about  10"  distant.  The  two  stars  at  the  extremities 
of  the  belt  are  also  double. 


36  LEPUS  AND   COLUMBA.  [§  43 

Orion  was  a  giant  and  mighty  hunter,  son  of  Neptune,  and  beloved 
by  both  Aurora  and  Diana.  The  legends  of  his  life  and  exploits  are 
numerous,  and  often  contradictory.  He  conquered  every  wild  beast 
except  the  Scorpion,  which  stung  and  killed  him.  As  a  winter  con- 
stellation his  influence  was  counted  stormy,  and  he  was  greatly  dreaded 
by  sailors. 

44.  Eridanus,  the  River  Po  (Map  II.).     January.  —  This  con- 
stellation lies  south  of  Taurus,  in  the  space  between  Cetus  and  Orion, 
and  extends  far  below  the  southern  horizon.     The  portion  near  the 
south  pole  has  a  pair  of  bright  stars,  which,  of  course,  are  never  visi- 
ble at  the  United  States.     Starting  with  Beta  (Cursa,  as  it  is  called), 
of  the  third  magnitude,  about  3°  north  and  a  little  west  of  Rigel,  one 
can  follow  a  sinuous  line  of  stars  westward  to  the  paws  of  Cetus, 
where  the  stream  turns  at  right  angles,  and  runs  southward  and  south- 
west to  the  horizon.     One  can  trace  it,  however,  only  by  the  help  of  a 
map  on  a  larger  scale  than  the  one  we  present. 

45.  Lepus  and  Columba  (Map  II.).     February.  —  The  con- 
stellation of  Lepus,  the  Hare,  one  of  Orion's  victims,  is  one 
of  the  ancient  forty-eight,  and  lies  just  south  of  the  giant, 
occupying  a  space  of  some  15°  square.     Its  characteristic  con- 
figuration is  a  quadrilateral  of  third  and  fourth  magnitude 
stars,  with  sides  from  3°  to  5°  long,  about  10°  south  of  Kappa 
Orionis,  and  15°  west  of  Sirius. 

Columba,  the  Dove,  lies  next  south  of  Lepus,  too  far  south 
to  be  well  seen  in  the  Northern  States.  Its  principal  star, 
Alpha  (Phact)  is  of  2^  magnitude,  and  is  readily  found  by 
drawing  a  line  from  Procyon  to  Sirius  and  prolonging  it 
about  the  same  distance.  In  passing,  we  may  note  that  a 
similar  line  drawn  from  Alpha  Orionis  through  Sirius,  and 
produced,  will  strike  near  Zeta  Argus,  or  Naos,  a  star  about 
as  bright  as  Phact,  —  the  two  lines  which  intersect  at  Sirius 
making  the  so-called  "Egyptian  X." 

Columba  is  a  modern  constellation,  commemorating  Noah's  dove 
returning  to  the  ark  with  the  olive  branch. 


§  46]  GEMINI  —  CANIS   MINOR.  37 

46.  Lynx  (Maps  I.,  II.,  and  III.).     February.  —  Returning  now 
to  the  northern  limit  of  the  map,  we  find  the  modern  constellation  of 
the  Lynx  lying  just  east  of  Auriga,  and  enveloping  it  on  the  north 
and  in  the  circumpolar  region,  as  shown  on  the  map.     It  contains  no 
stars  above  the  fourth  magnitude,  and  is  of  no  importance  except  as 
occupying  an  otherwise  vacant  space. 

47.  Gemini,  the  Twins  (Map  II.).     February  and  March. 
—  This  is  the  fourth,  of  the  zodiacal  constellations,  now  lying 
mostly  in  the  sign  of  Cancer.    It  contains  the  summer  solstitial 
point  —  the  point  where  the  sun  turns  from  its  northern  mo- 
tion to  its  southern  in  the  summer.     At  present  it  is  about  2° 
west  and  a  little  north  of  the  star  Eta.     Gemini  lies  northeast 
of  Orion  and  southeast  of  Auriga,  and  is  sufficiently  character- 
ized by  the  two  stars  Alpha  and  Beta  (about  4J-0  apart),  which 
mark  the  heads  of  the  twins.     The  southern  one,  Beta,  or 
Pollux,  is  now  the  brighter ;  but  Alpha,  Castor,  is  much  more 
interesting,  as  being  double   (easily  seen  with  a  small  tele- 
scope).    The  feet  are  marked  by  the  third-magnitude  stars 
Gamma  and  Mu,  some  10°  east  of  Zeta  Tauri. 

Castor  and  Pollux  were  the  sons  of  Jupiter  by  Leda,  and  ancient 
mythology,  especially  that  of  Rome,  is  full  of  legends  relating  to  them. 
Many  of  our  readers  will  remember  Macaulay's  ballad  of  "  The  Bat- 
tle of  Lake  Regillus,"  when  they  won  the  fight  for  Rome.  They  were 
regarded  as  the  special  patrons  of  the  sailor,  who  relied  much  on 
their  protection  against  the  evil  powers  of  Orion  and  the  Hyades. 

48.  Canis  Minor,  the  Little  Dog   (Map  III.).    March.  — 
This  constellation,  about  20°  south  of  Castor  and  Pollux,  is 
marked  by  the  bright  star  Procyon,  which  means  "  before  the 
dog,"  because  it  rises  about   half  an  hour   before   the   Dog 
Star,  Sirius.     Alpha,  Beta,  and  Gamma  form  together  a  config- 
uration closely  resembling  that  formed  by  Alpha,  Beta,  and 
Gamma  Arietis.      Procyon,  Alpha  Orionis,  and   Sirius  form 
nearly  an  equilateral  triangle,  with  sides  of  about  25°. 


38  CANIS  MAJOR.  [§  49 

The  animal  is  supposed  to  have  been  one  of  Orion's  dogs,  though 
some  say  the  dog  of  Icarus,  whom  they  identify  with  Bootes. 

49.  Canis  Major,  the  Great  Dog  (Map  II.).     February. — 
This    glorious    constellation    hardly   needs   description.      Its 
Alpha  is   the   Dog   Star,  Sirius,  beyond  all  comparison  the 
brightest  star  in  the  heavens,  and  one  of  our  nearer  neigh- 
bors, —  so  distant,  however,  that  it  requires  more  than  eight 
years  for  light  to  come  to  us  from  it.     It  is  nearly  pointed  at 
by  a  line  drawn  through  the  three  stars  of  Orion's  belt.    Beta, 
at  the  extremity  of  the  uplifted  paw,  is  of  the  second  magni- 
tude, and  so  are  several  of  the  stars  farther  south  in  the  rump 
and  tail  of  the  animal,  who  sits  up  watching  his  master  Orion, 
but  with  an  eye  out  for  Lepus. 

50.  Monoceros,  the  Unicorn  (Map  II.).     March.  —  This  is  one 
of  the  modern  constellations  organized  by  Hevelius  to  fill  the  gap 
between  Gemini  and  Canis  Minor  on  the  north,  and  Argo  Navis  and 
Canis  Major,  on  the  south.     It  lies  just  east  of  Orion,  and  has  no  con- 
spicuous stars,  but  is  traversed  by  a  brilliant  portion  of  the  Milky 
Way.     The  Alpha  of  the  constellation  (fourth  magnitude)  lies  about 
half-way  between  Alpha  Orionis  and  Sirius,  a  little  west  of  the  line 
that  joins  them.     11  Monocerotis,  a  fine  triple  star  (see  Fig.  76,  Art. 
366),  fourth  magnitude,  is  very  nearly  pointed  at  by  a  line  drawn  from 
Zeta  Canis  Majoris  northward  through  Beta,  and  continued  as  far 


51.  Argo  Navis,  the  Ship  Argo  (genitive  Argus)  (Maps 
II.  and  III.).  March.  — This  is  one  of  the  largest,  oldest,  and 
most  important  of  the  constellations,  lying  south  and  east  of 
Canis  Major.  Its  brightest  star,  Alpha  Argus,  Canopus,  ranks 
next  to  Sirius,  and  is  visible  in  the  Southern  States,  but  not 
in  the  Northern.  The  constellation,  huge  as  it  is,  is  only  a 
half  one,  like  Pegasus  and  Taurus,  —  only  the  stern  of  a  ves- 
sel, with  mast,  sail,  and  oars ;  the  stem  being  wanting.  In  the 
part  of  the  constellation  covered  by  our  maps  there  are  no 
very  conspicuous  stars,  though  there  are  some  of  third  and 


§  51]  CANCER  —  LEO.  39 

fourth  magnitude  which  lie  east  and  southeast  of  the  rump 
and  tail  of  Canis  Major.  We  have  already  mentioned  Zeta,  or 
Naos,  at  the  southeast  extremity  of  the  "  Egyptian  X." 

According  to  the  Greek  legends,  this  is  the  miraculous  ship  in 
which  Jason  and  his  fifty  companions  sailed  from  Greece  to  Colchis 
to  recover  the  Golden  Fleece.  It  had  in  its  bow  a  piece  of  oak  from 
the  sacred  grove  of  Dodona,  which  enabled  the  ship  to  talk  with  its 
commander  and  give  him  advice. 

Some  see  in  the  constellation  the  ark  of  Noah. 

52.  Cancer,  the  Crab  (Maps  II.  and  III.)     March.  —  This 
is  the  fifth  of  the  zodiacal  constellations,  lying  just  east  of 
Canis  Minor.     It  does  not  contain  a  single  conspicuous  star, 
but  is  easily  recognizable  from  its  position,  and  in  a  dark  night 
by  the  nebulous  cloud  known  as  Prcesepe,  or  the  "Manger," 
with  the  two  stars  Gamma  and  Delta  near  it,  —  the  so-called 
Aselli,  or  "Donkeys."      Praesepe,   sometimes  also  called  the 
"Beehive,"  is  really  a  coarse  cluster  of  seventh  and  eighth 
magnitude  stars,  resolvable  by  an  opera-glass.     The  line  from 
Castor  through  Pollux,  produced  about  12°,  passes  near  enough 
to  it  to  serve  as  a  pointer. 

The  star  Zeta  is  a  very  pretty  triple  star,  though  with  a  small  tel- 
escope it  can  be  seen  only  as  double.  It  is  easily  found  by  a  line 
from  Castor  through  Pollux,  produced  2J  times  as  far. 

By  the  Greeks  this  was  identified  as  the  Crab  who  attacked  Hercu- 
les when  he  was  fighting  the  Lernaean  Hydra.  In  the  old  Egyptian 
zodiacs  the  Crab  is  replaced  by  the  Scarabaeus,  or  Beetle ;  and  in  some 
of  the  more  recent  zodiacs  by  a  pair  of  asses,  still  recognized  in  the 
name,  Aselli,  given  to  the  two  stars  Gamma  and  Delta. 

53.  Leo,   the  Lion  (Map  III.).      April.— East  of  Cancer 
lies  the  noble  constellation  of  Leo,  which  adorns  the  evening 
sky  in  March  and  April ;  it  is  the  sixth  of  the  zodiacal  constel- 
lations,  now  occupying  the  sign  of  Virgo.     Its  leading  star, 
Regulus,  or  "Cor  Leonis,"  is  of  the  first  magnitude,  and  two 
others,  Beta  (Denebola)  and  Gamma,  are  of  the  second  mag- 


40  HYDEA.  [§  53 

nitude.  Alpha,  Gamma,  Delta,  and  Beta  form  a  conspicuous 
irregular  quadrilateral  (see  map),  the  line  from  Eegulus  to 
Denebola  being  about  26°  long.  Another  characteristic  con- 
figuration is  "the  Sickle,"  of  which  Eegulus  is  the  handle, 
and  the  curved  line  Eta,  Gamma,  Zeta,  Mu,  and  Epsilon,  is  the 
blade,  the  cutting  edge  being  turned  towards  Cancer. 

The  "radiant"  of  the  November  meteors  lies  between  Zeta  and 
Epsilon.  Gamma,  in  the  Sickle,  and  at  the  southeast  corner  of  the 
quadrilateral,  is  a  very  pretty  double  star,  binary,  with  a  period  of 
about  400  years. 

According  to  classic  writers,  this  is  the  Nemaean  Lion  which  was 
killed  by  Hercules,  as  the  first  of  his  Twelve  Labors ;  but,  like  Aries 
and  Taurus,  the  constellation  is  far  older  than  the  Greeks,  and  stands 
in  its  present  form  on  all  the  ancient  zodiacs. 

54.  Leo  Minor  and  Sextans  (Map  II.).     April.  —  Leo  Minor, 
the  Smaller  Lion,  is  an  insignificant  modern  constellation  composed  of 
a  few  small  stars  north  of  Leo,  between  it  and  the  feet  of  Ursa  Major. 
It  contains  nothing  deserving  special  notice.     The  same  remark  holds 
good  as  to  Sextans,  the  Sextant,  and  even  more  emphatically. 

55.  Hydra  (Map  III.).    March  to  June.  —  This  constellation, 
with  its  riders,  Crater  (the  Cup)  and  Corvus  (the  Raven),  is  a 
large  and  important  one,  though  not  very  brilliant.     The  head 
is  marked  by  a  group  of  five  or  six  fourth  and  fifth  magnitude 
stars  just  15°  south  of  Prsesepe.     A  curving  line  of  small  stars 
leads  down  southeast  to  Alpha,  Cor  Hydras,  or  Alphard,  a  2J 
magnitude  star  standing  very  much  alone.     From  there,  as 
the  map  shows,  an  irregular  line  of  fourth-magnitude  stars 
running  far  south  and  then  east,  almost  to  the  boundary  of 
Scorpio,  marks  the  creature's  body  and  tail,  the  whole  cover- 
ing almost  six  hours  of  right  ascension,  and  very  nearly  90° 
of  the  sky.     About  the  middle  of  the  length  of  Hydra,  and 
just  below  the  hind  feet  of  Leo  (30°  due  south  from  Denebola), 
we  find  the  little  constellation  of  Crater;  and  just  east  of  it 
the  still  smaller  but  much  more  conspicuous  one  of  Corvus, 


§  55]  VIRGO.  41 

with  two  second-magnitude  stars  in  it,  and  four  of  the  third 
and  fourth  magnitudes.  It  is  well  marked  by  a  characteristic 
quadrilateral  (see  map),  with  Delta  and  Eta  together  at  its 
northeast  corner.  The  order  of  the  letters  in  Corvus  differs 
widely  from  that  of  brightness,  suggesting  that  changes  may 
have  occurred  since  the  letters  were  applied. 

Epsilon  Hydrae  and  Delta  Corvi  are  pretty  double  stars,  the  latter 
easily  seen  with  a  small  telescope ;  colors,  yellow  and  purple. 

Hydra,  according  to  the  Greeks,  is  the  immense  hundred-headed 
monster  which  inhabited  the  Lernaean  Marsh,  and  was  killed  by  Her- 
cules as  his  second  labor.  But  the  Hydra  of  the  heavens  has  only  one 
head,  and  is  probably  much  older  than  the  legends  of  Hercules. 

An  old  legend  says  that  Corvus  is  Coronis,  a  nymph  who  was  trans- 
formed into  a  raven  to  escape  the  pursuit  of  Neptune.  Another  story 
,  is  that  she  was  changed  into  a  crow  for  telling  tales  of  some  impru- 
dent actions  that  came  under  her  notice. 

56.  Virgo  (Map  III.).  May.  —  East  and  south  of  Leo  lies 
Virgo,  the  seventh  zodiacal  constellation,  mostly  in  the  sign 
of  Libra.  Its  Alpha,  Spica  Virginis,  is  of  the  1^  magnitude, 
and,  standing  rather  alone,  10°  south  of  the  celestial  equator, 
is  easily  recognized  as  the  southern  apex  of  a  nearly  equilat- 
eral triangle  which  it  forms  with  Denebola  (Beta  Leonis)  to 
the  northwest,  and  Arcturus  northeast  of  it.  Beta  Virginis,  of 
the  third  magnitude,  is  14°  south  of  Denebola.  A  line  drawn 
eastward  and  a  little  south  from  Beta  (third  magnitude)  and 
then  carried  on,  curving  northward,  passes  successively  (see 
map)  through  Eta,  Gamma,  Delta,  and  Epsilon,  of  the  third 
magnitude.  (Notice  the  word  Begde,  like  Bagdei  in  Cassio- 
peia, Art.  28.) 

Gamma  is  a  remarkable  binary  star,  at  present  easily  visible  as 
double  in  a  small  telescope.  Its  period  is  one  hundred  and  eighty-five 
years,  and  it  has  completed  pretty  nearly  a  full  revolution  since  its 
first  discovery.  For  a  diagram  of  its  orbit,  see  Fig.  77,  Art.  369.  A 
few  degrees  north  of  Gamma  lies  the  remarkable  nebulous  region  of 


42  CANES   VENATICI. 


[§56 


Virgo,  containing  hundreds  of  these  curious  objects  ;  but  for  the  most 
part  they  are  very  faint,  and  observable  only  with  large  telescopes. 

The  classic  poets  recognize  Virgo  as  Astrsea,  the  goddess  of  justice, 
who,  last  of  all  the  old  divinities,  left  the  earth  at  the  close  of  the 
Golden  Age.  She  holds  the  Scales  of  Justice  (Libra)  in  one  hand, 
and  in  the  other  a  sheaf  of  wheat. 

Some  identify  her  with  Erigone,  the  daughter  of  Icarus  or  Bootes. 
Others  recognize  in  her  the  Egyptian  Isis. 

57.  Coma  Berenices,  Berenice's  Hair  (Map  III.).    May.  —  This 
little  constellation,  composed  of  a  great  number  of  fifth  and  sixth 
magnitude  stars,  lies  30°  north  of  Gamma  and  Eta  Virginis,  and  about 
15°  northeast  of  Denebola.      It   contains   a  number  of    interesting 
double  stars,  but  they  are  not  easily  found  without  the  help  of  a  tele- 
scope equatorially  mounted. 

The  constellation  was  established  by  the  Alexandrian  astronomer 
Conon,  in  honor  of  the  queen  of  Ptolemy  Soter.  She  dedicated  her 
splendid  hair  to  the  gods,  to  secure  her  husband's  safety  in  war. 

58.  Canes  Venatici,  the  Hunting-Dogs  (Map  III.).     May. — 

These  are  the  dogs  with  which  Bootes,  the  huntsman,  is  pursu- 
ing the  Great  Bear  around  the  pole  :  the  northern  of  the  two 
is  Asterion,  the  southern  Chara.  Most  of  the  stars  are  small, 
but  Alpha  is  of  the  2^  magnitude,  and  is  easily  found  by  draw- 
ing from  Eta  Ursse  Majoris  (the  star  in  the  end  of  the  Dipper- 
handle)  a  line  to  the  southwest,  perpendicular  to  the  line  from 
Eta  to  Zeta  (Mizar),  and  about  15°  long  :  in  England  it  is  gen- 
erally known  as  Cor  Caroli  (the  Heart  of  Charles),  in  allusion 
to  Charles  I.  With  Arcturus  and  Denebola  it  forms  a  triangle 
much  like  that  which  they  form  with  Spica. 

The  remarkable  whirlpool  nebula  of  Lord  Rosse  is  situated  in  this 
constellation,  about  3°  west  and  somewhat  south  of  the  star  Eta  Ursse 
Majoris.  In  a  small  telescope  it  is  by  no  means  conspicuous,  but  in  a 
large  telescope  is  a  wonderful  object. 

The  constellation  is  modern,  formed  by  Hevelius. 

59.  Bootes,  the  Huntsman  (Maps  I.  and  III.).    June. — This 
fine  constellation  extends  more  than  60°  in  declination,  from 


§  59]  CORONA   BOREALIS.  43 

near  the  equator  quite  to  Draco,  where  the  uplifted  hand  hold- 
ing the  leash  of  the  hunting-dogs  overlaps  the  tail  of  the  Bear. 
Its  principal  star,  Alpha,  Arcturus  (meaning  ' bear-driver'),  is 
of  a  ruddy  hue,  and  in  brightness  is  excelled  only  by  Sirius 
among  the  stars  visible  in  our  latitudes.  It  is  at  once  recog- 
nizable by  its  forming  with  Spica  and  Denebola  the  great  tri- 
angle already  mentioned  (Art.  56).  Six  degrees  west  and  a 
little  south  of  it  is  Eta,  of  the  third  magnitude,  which  forms 
with  it,  in  connection  with  Upsilon,  a  configuration  like  that 
in  the  head  of  Aries.  Epsilon  is  about  10°  northeast  of  Arc- 
turus, and  in  the  same  direction  about  10°  farther  lies  Delta. 
The  map  shows  the  pentagon  which  is  formed  by  these  two 
stars  along  with  Beta,  Gamma,  and  Rho. 

Epsilon  is  a  fine  double  star ;  colors,  orange  and  greenish  blue ; 
distance,  about  3". 

The  legendary  history  of  this  constellation  is  very  confused.  One 
legend  makes  it  to  be  Icarus,  the  father  of  Erigone  (Virgo).  But  the 
one  most  usually  accepted  makes  it  to  be  Areas,  son  of  Callisto.  After 
she  was  changed  to  a  bear  (Ursa  Major),  her  son,  not  recognizing  her, 
hunted  her  with  his  dogs,  and  was  on  the  point  of  killing  her,  when 
Jupiter  interfered  and  took  them  both  to  the  stars. 

60.  Corona  Borealis,  the  Northern  Crown  (Map  III.).  June. 
—  This  beautiful  little  constellation  lies  20°  northeast  of  Arc- 
turus, and  is  at  once  recognizable  as  an  almost  perfect  semi- 
circle composed  of  half  a  dozen  stars,  among  which  the  bright- 
est, Alpha  (Gemma  or  Alphacca),  is  of  the  second  magnitude. 
The  extreme  northern  one  is  Theta ;  next  comes  Beta,  and  the 
rest  follow  in  the  Bagdei  order,  just  as  in  Cassiopeia.  About  a 
degree  north  of  Delta,  now  visible  with  an  opera-glass,  is  a 
small  star  which  in  1866  suddenly  blazed  out  until  it  became 
brighter  than  Alphacca  itself  (see  Art.  355). 

The  little  star  Eta  is  a  rapid  binary  with  a  period  of  less  than  forty- 
two  years.  At  times  it  can  be  easily  divided  by  a  small  telescope. 

The  constellation  is  said  to  be  the  crown  that  Bacchus  gave  to 
Ariadne,  before  he  deserted  her  on  the  island  of  Naxos. 


44  LIBRA  —  CENTAUR  US.  [§  61 

61.  Libra,  the  Balance   (Map  III.).     June.  —  This  is  the 
eighth   of  the  zodiacal  constellations,   lying  east   of  Virgo, 
bounded  on  the  south  by  Centaurus  and  Lupus,  on  the  east  by 
the  upstretched  claw  of  Scorpio,  and  on  the  north  by  Serpens 
and  Virgo.     It  is  inconspicuous,  the  most  characteristic  figure 
being  the  trapezoid  formed  by  the  lines  joining  the  stars  Alpha, 
Iota,  Gamma,  and  Beta.     Beta,  which  is  the  northern  one,  is 
about  30°  due  east  from  Spica,  while  Alpha  is  about  10°  south- 
west of  Beta.     The  remarkable  variable,  Delta  Librae,  is  4° 
west  and  a  little  north  from  Beta.     Most  of  the  time  it  is  of 
the  4±  or  5  magnitude,  but  runs  down  nearly  two  magnitudes, 
to  invisibility,  at  the  minimum,  once  in  2J-  days. 

Libra  is  the  Balance  of  Virgo,  the  goddess  of  justice,  and  was  not 
recognized  by  the  classic  writers  as  a  separate  constellation  until  the 
time  of  Julius  Caesar ;  the  space  now  occupied  by  Libra  being  then 
covered  by  the  extended  claws  of  Scorpio. 

62.  Antlia,  Centaurus,  and  Lupus    (Map  III.).     April  to 
June.  —  These  constellations  lie  south  of  Hydra  and  Libra. 

Antlia  Pneumatica  (the  Air-Pump)  is  a  modern  constellation  of  no 
importance  and  hardly  recognizable  by  the  eye,  having  only  a  single 
star  as  bright  as  the  4£  magnitude. 

Centaurus,  on  the  other  hand,  is  an  ancient  and  extensive 
asterism,  containing  in  its  south  (circumpolar)  regions,  not 
visible  in  the  United  States,  two  stars  of  the  first  magnitude, 
Alpha  and  Beta.  Alpha  Centauri  stands  next  after  Sirius  and 
Canopus  in  brightness,  and,  as  far  as  present  knowledge  indi- 
cates, is  our  nearest  neighbor  among  the  stars.  The  part  of  the 
constellation  which  becomes  visible  in  our  latitudes  is  not 
especially  brilliant,  though  it  contains  several  stars  of  the  2j- 
and  3  magnitudes  in  the  region  lying  south  of  Corvus  and 
Spica  Virginis. 

Lupus,  the  Wolf,  also  one  of  Ptolemy's  constellations,  lies  due  east 
of  Centaurus  and  just  south  of  Libra.  It  contains  a  considerable 


§  62]  SCOEPIO.  45 

number  of  third  and  fourth  magnitude  stars ;  but  it  is  too  low  for 
any  satisfactory  study  in  our  latitudes.  It  is  best  seen  late  in  June. 
These  constellations  contain  numerous  objects  interesting  for  a  south- 
ern observer,  but  not  observable  by  us. 

The  Centaurs  were  a  fabulous  race,  half  man,  half  horse,  who  lived 
in  Thessaly  and  herded  cattle.  Chiron  was  the  most  distinguished  of 
them,  the  teacher  of  almost  all  the  Greek  heroes  in  every  manly  and 
noble  art,  and  the  friend  of  Hercules,  by  whom,  however,  he  was  acci- 
dentally killed.  Jupiter  transferred  him  to  the  stars.  (See  Sagitta- 
rius, Art.  72.)  The  wolf  is  represented  as  transfixed  by  the  Centaur's 
spear. 

63.  Scorpio  (or  Scorpius;  genitive  Scorpii),  the  Scorpion 
(Map  IV.).  July.  —  This,  the  ninth  of  the  zodiacal  constel- 
lations and  the  most  brilliant  of  them  all,  lies  southeast  of 
Libra,  which  in  ancient  times  used  to  form  its  claws  (Chelae). 
It  is  recognized  at  once  by  the  peculiar  configuration  of  the 
stars,  which  resembles  a  boy's  kite,  with  a  long  streaming  tail 
extending  far  down  to  the  south  and  east,  and  containing  sev- 
eral pairs  of  stars.  The  principal  star  of  the  constellation, 
Antares,  is  of  the  first  magnitude,  and  fiery  red  like  the  planet 
Mars.  From  this  it  gets  its  name,  which  means  "the  rival 
of  Ares"  (Mars).  Antares  is  a  very  pretty  double  star,  with 
a  beautiful  little  green  companion  just  to  the  west  of  it,  not 
very  easy  to  be  seen,  however,  with  a  small  telescope.  Beta 
(second  magnitude)  is  in  the  arch  of  the  kite  bow,  about  8°  or 
9°  northwest  of  Antares,  while  the  star  which  Bayer  lettered 
as  Gamma  Scorpii  is  well  within  Libra,  20°  west  of  Antares. 
(There  is  considerable  confusion  among  uranographers  as  to 
the  boundary  between  the  two  constellations.)  The  other 
principal  stars  of  the  constellation  are  easily  found  on  the 
map. 

Many  of  them  are  of  the  second  magnitude.  One  of  the  finest 
clusters  known,  and  easily  seen  with  a  small  telescope,  is  Messier  80, 
which  lies  about  half-way  between  Alpha  and  Beta. 

According  to  the  Greek  mythology,  this  is  the  scorpion  that  killed 


46  OPHIUCHUS   AND   SERPENS.  [§  63 

Orion.  It  was  the  sight  of  this  monster  of  the  heavens  that  frightened 
the  horses  of  the  sun,  when  poor  Phaeton  tried  to  drive  them  and  was 
thrown  out  of  his  chariot.  Among  astrologers,  the  influence  of  Scorpio 
has  always  been  held  as  baleful  to  the  last  degree. 

64.  Norma  Nilotica,  the  rule  with  which  the  height  of  the  Nile 
was  measured,  lies  west  of  Scorpio,  while  Ara  lies  due  south  of  Eta 
and  Theta.     Both  are  old  Ptolemaic  constellations,  but  are  small  and 
of  little  importance,  at  least  to  observers  in  our  latitudes. 

65.  Ophiuchus  and  Serpens  (Map  IV.).     July.  —  Ophiuchus 
means  the  "  serpent-holder,"  and  probably  refers  to  the  great 
physician,  JSsculapius.     The  hero  is  represented  as  standing 
with  his  feet  on  Scorpio,  and  grasping  the  "  serpent."     The 
two  constellations,  therefore,  are  best  treated  together.     The 
head  of  Serpens  is  marked  by  a  group  of  small  stars  lying  just 
south  of  Corona  and  20°  due  east  of  Arcturus.      Beta  and 
Gamma  are  the  two  brightest  stars  in  the  group,  their  magni- 
tudes 3^  and  4.     Delta  lies  6°  southwest  of  Beta,  and  there 
the  Serpent's  body  bends  southeast  through  Alpha  and  Epsilon 
Serpentis   (see  map)   to  Delta  and  Epsilon  Ophiuchi  in  the 
giant's  hand.     The  line  of  these  five  stars  carried  upwards 
passes  nearly  through  Epsilon  Bootis,  and  downwards  through 
Zeta  Ophiuchi.     A  line  crossing  this  at  right  angles,  nearly 
midway  between  Epsilon  Serpentis  and  Delta  Ophiuchi,  passes 
through  Mu  Serpentis  on  the  southwest  and  Lambda  Ophiuchi 
to  the  northeast.      The  lozenge-shaped  figure  formed  by  the 
lines  drawn  from  Alpha  Serpentis  and  Zeta  Ophiuchi  to  the 
two  stars  last  mentioned  is  one  of  the  most  characteristic 
configurations  of  the  summer  sky.      Alpha  Ophiuchi  (2}  mag- 
nitude)   (Mas  Alaghue)   is  easily  recognizable  in  connection 
with  Alpha  Herculis,  since  they  stand  rather  isolated,  about  6° 
apart,  on  the  line  drawn  from  Arcturus  through  the  head  of 
Serpens,  and  produced  as  far  again.     Alpha  Ophiuchi  is  the 
eastern  and  the  brighter  of  the  two,  and  forms  with  Vega  and 
Altair  a  nearly  equilateral  triangle.     Beta  Ophiuchi  lies  about 
9°  southeast  of  Alpha. 


§  65]    ^  HERCULES.  47 

Five  degrees  east  and  a  little  south  of  Beta  are  five  small  stars  in 
the  Milky  Way,  forming-  a  V  with  the  point  to  the  south,  much  like 
the  Hyades  of  Taurus.  They  form  the  head  of  the  now  discredited 
constellation,  "  Poniatowski's  Bull"  (Taurus  Poniatovii),  proposed  in 
1777,  and  found  in  many  maps.  70  Ophiuchi  (the  middle  star  in  the 
eastern  leg  of  the  V  of  Poniatowski's  Bull)  is  a  very  pretty  double  star, 
binary,  with  a  period  of  ninety-three  years.  Just  at  present  the  star 
is  too  close  to  be  resolved  by  a  small  instrument,  but  it  will  soon  open 
up  again. 

Ophiuchus  is  identified  with  JEsculapius,  who  was  the  first  great 
physician,  the  son  of  Apollo  and  the  nymph  Coronis,  educated  in  the 
art  of  medicine  by  Chiron,  the  Centaur.  The  serpent  and  the  cock 
were  sacred  to  him  in  his  character  as  a  deity.  But  the  constellation 
is  older  than  the  classic  legends. 

66.  Hercules  (Maps  i.  and  IV.).  July.  —  This  noble  con- 
stellation lies  next  north  of  Ophiuchus,  between  it  and  Draco. 
The  hero  is  represented  as  resting  on  one  knee,  with  his  foot 
on  the  head  of  Draco,  while  his  head  is  close  to  that  of  Ophiu- 
chus. The  constellation  contains  no  stars  of  the  first  or  even 
of  the  second  magnitude,  but  there  are  a  number  of  the  third. 
The  most  characteristic  figure  is  the  keystone-shaped  quadri- 
lateral formed  by  the  stars  Epsilon,  Zeta,  Eta,  with  Pi  and 
Eho  together  at  the  northeast  corner.  It  lies  about  midway 
on  the  line  from  Vega  to  Corona. 

On  its  western  boundary,  a  third  of  the  way  from  Eta  towards  Zeta, 
lies  the  remarkable  cluster,  Messier  13,  —  on  the  whole  the  finest  of 
all  star  clusters,  —  barely  visible  to  the  naked  eye  on  a  dark  night. 
Alpha  Herculis  (Ras  Algethi),  in  the  head  of  the  giant,  is  a  very 
beautiful  double  star,  colors  orange  and  blue,  distance  about  5".  It 
is  slightly  variable,  and  has  a  remarkable  spectrum,  characterized  by 
numerous  dark  bands. 

Hercules,  the  son  of  Jupiter  and  Alcmena  (a  granddaughter  of 
Andromeda),  was  the  Greek  incarnation  of  gigantic  strength.  His 
heroic  actions  and  freaks  occupy  more  space  in  their  mythology  than 
those  of  any  personage  except  Jupiter  himself.  He  was  the  pupil  of 
Chiron,  but  by  the  will  of  Jupiter,  his  father,  was  subjected  to  the 


48  LYRA  —  CYGNUS.  [§  66 

power  of  Eurystheus,  the  king  of  Tiryiis,  for  many  years.  At  his 
bidding  he  performed  the  great  enterprises  known  as  the  Twelve 
Labors  of  Hercules,  for  which  we  must  refer  the  reader  to  the  Classi- 
cal Dictionaries.  Among  them  we  have  already  mentioned  the  con- 
quest of  the  Nemaean  Lion  and  of  the  Lernsean  Hydra.  Another  was 
to  bring  from  the  garden  of  the  Hesperides  the  golden  apples  which 
were  guarded  by  the  dragon  that  he  killed,  and  on  which  his  feet  rest 
in  the  sky.  His  last  and  greatest  achievement  was  to  bring  to  the 
earth  the  three-headed  dog,  Cerberus,  the  guardian  of  the  infernal 
regions. 

67.  Lyra  (Map  IV.).     August.  —  This  constellation  is  suffi- 
ciently marked  by  the  great  white  or  blue  star,   Vega,  one  of 
the  finest  stars  in  the  whole  sky,  and  certainly  many  times 
larger  than  our  own  sun.     It  is  attended  on  the  east  by  two 
fourth-magnitude  stars,  Epsilon  and  Zeta,  which  form  with  it 
a  little  equilateral  triangle  having  sides  about  2°  long.     Epsi- 
lon is  a  double-double  or  quadruple  star.     A  sharp  eye,  even 
unaided  by  a  telescope,  divides  the  star  into  two,  and  a  large 
telescope  splits  each  of  the  components.     It  is  a  very  pretty 
object  even  to  a  small  telescope.     Beta"  and  Gamma,  of  the 
third  magnitude  (Beta  is  variable),  lie  about  8°  southeast  from 
Vega,  2y  apart.     (See  Art.  357.) 

On  the  line  between  Beta  and  Gamma,  one-third  of  the  way  from 
Beta,  lies  Messier  57,  the  Annular  Nebula,  which  can  be  seen  as  a 
small  hazy  ring  even  by  a  small  telescope,  though  of  course  it  is  much 
more  interesting  with  a  larger  one. 

According  to  the  legends  this  constellation  is  the  lyre  of  Orpheus, 
with  which  he  charmed  the  stern  gods  of  the  lower  world,  and  per- 
suaded them  to  restore  to  him  his  lost  Eurydice. 

68.  Cygnus   (Maps   I.   and  IV.).     September. — This   con- 
stellation lies  due  east  from  Lyra,  and  is  easily  recognized  by 
the  cross  that  marks  it.     The  bright  star  Alpha  (1^  magni- 
tude) is  at  the  top,  and  Beta  (third  magnitude)  at  the  bottom, 
while  Gamma  is  where  the  cross-bar  from  Delta  to  Epsilon 
intersects  the  main   piece,  which  lies  along  the  Milky  Way 


§  68]  VULPECULA  ET  ANSER.  49 

from  the  northeast  to  the  southwest.  Beta  (Albireo)  is  a 
beautiful  double  star,  orange  and  dark  blue,  one  of  the  finest 
of  the  colored  pairs  for  a  small  telescope.  61  Cygni,  which  is 
memorable  as  the  first  star  to  have  its  parallax  determined  (by 
Bessel  in  1838),  is  easily  found  by  completing  the  parallelo- 
gram of  which  Alpha,  Gamma,  and  Epsilon  are  the  other  three 
corners.  Sigma  and  Tau  form  a  little  triangle  with  61,  which 
is  the  faintest  of  the  three.  61  is  a  fine  double  star.  Delta 
is  also  a  fine  double,  but  too  difficult  for  an  instrument  of  less 
than  six  inches'  aperture. 

According  to  Ovid,  Cygnus  was  a  friend  of  Phaeton's,  who  mourned 
his  unhappy  fate  and  was  changed  to  a  swan.  Others  see  in  the  con- 
stellation the  swan  in  whose  form  Jupiter  visited  Leda,  the  mother  of 
Castor  and  Pollux  and  of  Helen  of  Troy. 

69.  Vulpecula  et  Anser,  the  Fox  and  the  Goose  (Map  IV.). 
September.  —  This  little  constellation  is  one  of  those  originated  by 
Hevelius,  and  has  obtained  more  general  recognition  among  astrono- 
mers than  most  of  his  creations.     It  lies  just  south  of  Cygnus,  and  is 
bounded  to  the  south  by  Delphinus,  Sagitta,  and  Aquila.     It  has  no 
conspicuous    stars,  but   it  contains    one  very  interesting    telescopic 
object,  —  the  "  Dumb-bell  Nebula"  (see  map).     It  may  be  found  on  a 
line  from  Gamma  Lyrae  through  Beta  Cygni,  produced  as  far  again. 

70.  Sagitta  (Map  IV.).    August. — -This  little  constellation,  though 
very  inconspicuous,  is  one  of  the  old  48.     It  lies  south  of  Vulpecula, 
and  the  two  stars  Alpha  and  Beta,  which  mark  the  feather  of  the 
arrow,  lie  nearly  midway  between  Beta  Cygni  and  Altair,  while  its 
point  is  marked  by  Gamma,  5°  farther  east  and  north.     Beta,  the 
middle  star  of  the  shaft  of  the  arrow,  is  a  very  pretty  double  star,  dis- 
tance about  8"  :  the  larger  star  is  itself  a  close  double. 

71.  A'quila    (not   A-qui'la)    (Map    IV.).      August.  —  This 
constellation  lies  on  the  celestial  equator,  east  of  Ophiuchus 
and  north  of  Sagittarius  and  Capricornus.     Its  characteristic 
configuration  is  that  formed  by  Alpha,  Altair,  with  Gamma  to 
the  north  and  Beta  to  the  south.    It  lies  about  20°  south  of  Beta 


50  SAGITTARIUS.  [§  71 

Cygni,  and  forms  a  fine  triangle  with  Beta  and  Alpha  Ophiu- 
chi.  Altair  is  taken  as  the  standard  first-magnitude  star.  Of 
course,  several  of  those  which  are  called  first  magnitude,  like 
Sirius  and  Vega,  are  very  much  brighter  than  this,  while  others 
fall  considerably  below  it. 

Aquila  was  the  bird  of  Jupiter,  which  he  kept  by  the  side  of  his 
throne  and  sent  to  bring  Ganymede  to  him. 

The  southern  part  of  the  region  allotted  to  Aquila  on  our  maps  has 
been  assigned  to  Antinoiis,  which  is  recognized  on  some  celestial 
globes.  The  constellation  existed  even  in  Ptolemy's  time,  but  he 
declined  to  adopt  it.  Hevelius  has  appropriated  the  eastern  part  of 
Antinoiis  for  his  constellation  of  Scutum  Sobieski. 

72.  Sagittarius,  the  Archer  (Map  IV.).  August.  —  This, 
the  tenth  of  the  zodiacal  constellations,  contains  no  stars  of  the 
first  magnitude,  but  a  number  of  the  second  and  third  magni- 
tude, which  make  it  reasonably  conspicuous.  The  most  char- 
acteristic configuration  is  the  little  inverted  "  milk-dipper/' 
formed  by  the  five  stars,  Lambda,  Phi,  Sigma,  Tau,  and  Zeta, 
of  which  the  last  four  form  the  bowl,  while  Lambda  (in  the 
Milky  Way)  is  the  handle  (see  map).  Delta,  Gamma,  and 
Epsilon,  which  form  a  triangle,  right-angled  at  Delta,  lie  south 
and  a  little  west  of  Lambda,  the  whole  eight  together  forming 
a  very  striking  group.  There  is  a  curious  disregard  of  any 
apparent  principle  in  the  lettering  of  the  stars  of  this  con- 
stellation ;  Alpha  and  Beta  are  stars  not  exceeding  in  bright- 
ness the  fourth  magnitude,  about  4°  apart  on  a  north  and  south 
line,  and  lying  some  15°  south  and  5°  east  of  Zeta  (see  map), 
while  Sigma  is  now  a  bright  second-magnitude  star,  strongly 
suspected  of  being  irregularly  variable.  (The  constellation 
contains  an  unusual  number  of  known  variables.)  The  Milky 
Way  in  Sagittarius  is  very  bright  and  complicated  in  structure, 
full  of  knots  and  streamers  and  dark  pockets,  and  containing 
many  beautiful  and  interesting  objects. 

This  constellation  is  said  by  many  writers  to  commemorate  the 
Centaur,  Chiron,  but  the  same  constellation  appears  on  the  ancient 


§  72J  CAPRICORNUS  —  DELPHINUS.  51 

zodiacs  of  Egypt  and  India,  and  it  seems  probable,  therefore,  that, 
like  the  Bull  and  the  Lion,  it  was  not  representative  of  any  particular 
individual. 

73.  Capricornus  (Map  IV.).  September. — This,  the  eleventh 
of  the  zodiacal  constellations,  follows  Sagittarius  on  the  east. 
It  has  no  bright  stars,  but  the  configuration  formed  by  the  two 
Alphas  (ax  and  a2)  with  each  other  and  with  Beta,  3°  south,  is 
characteristic,  and  not  easily  mistaken  for  anything  else.     The 
two  Alphas,  a  pretty  double  to  the  naked  eye,  lie  on  the  line 
drawn  from  Beta  Cygni  (at  the  foot  of  the  cross)  through 
Altair,  and  produced  about  25°. 

Some  say  that  this  constellation  represents  the  god  Pan,  who  was 
represented  by  the  Greeks  as  having  the  legs  of  a  goat  and  the  head  of 
a  man.  Others  find  in  the  goat,  Amalthea  (the  foster-mother  of  the 
infant  Jupiter),  who  is  also,  it  will  be  remembered,  represented  in  the 
constellation  of  Auriga. 

74.  Delphinus,  the  Dolphin  (Map  IV.).     September.  —  This 
constellation,  though  small,  is  one  of  the  ancient  48,  and  is 
unmistakably  characterized  by  the  rhombus  of  third-magnitude 
stars  known  as  "  Job's  Coffin.'7    It  lies  about  15°  east  of  Altair. 
There  are  a  few  stars  visible  to  the  naked  eye,  in  addition  to 
the  four  that  form  the  rhombus.     Epsilon,  about  3°  to  the 
southwest,  is  the  only  conspicuous  one. 

Gamma,  at  the  northwest  angle  of  the  rhombus,  is  a  very  pretty 
double  star.  Beta  is  also  a  very  close  and  rapid  binary,  beyond  the 
reach  of  all  but  large  telescopes. 

This  is  the  Dolphin  that  preserved  the  life  of  the  musician,  Arion, 
who  was  thrown  into  the  sea  by  sailors,  but  carried  safely  to  land 
upon  the  back  of  the  compassionate  fish,  who  loved  his  music. 

75.  Equuleus,  the  Little  Horse    (Map  IV.).     This  little  con- 
stellation, simply  a  horse's  head,  though  still  smaller  than  the  Dolphin 
and  less  conspicuous,  is  also  one  of  Ptolemy's.     It  lies  about  20°  due 
east  of  Altair,  and  10°  southeast  of  the  Dolphin  (see  map) . 


52  PEGASUS  —  AQUARIUS.  [§  76 

76.  Lacerta,  the   Lizard    (Maps   I.   and   IV.).     This  is  one  of 
Hevelius's  modern  constellations,  lying  between  Cygnus  and  Androm- 
eda, with  no  stars  above  the  4£  magnitude,  and  of  no  importance  for 
our  purposes. 

77.  Pe'gasus  (not  Pe-gas'us)   (Map  IV.).     October. — This 
winged  horse  covers  an  immense  space.     Its  most  notable  con- 
figuration is  the  "great  square,"  formed  by  the  second-mag- 
nitude stars,  Alpha  (Markab),  Beta,  and  Gamma  Pegasi,  in 
connection  with  Alpha  Andromedse  (sometimes  lettered  Delta 
Pegasi),  at  its  northeast  corner.    The  stars  of  the  square  lie  in 
the  body  of  the  horse,  which  has  no  hindquarters.  A  line  drawn 
from  Alpha  Andromedae  through  Alpha  Pegasi,  and  produced 
about  an  equal  distance,  passes  through  Xi  and  Zeta  in  the 
animal's  neck,  and  reaches   Theta  in  his  ear.     Epsilon   (or 
Enif),  the  bright  star  8°  northwest  of  Theta,  marks  his  nose. 
The  forelegs  are  in  the  northwestern  part  of  the  constellation 
just  east  of  Cygnus,  and  are  marked,  one  of  them  by  the  stars 
Eta  and  Pi,  and  the  other  by  Iota  and  Kappa. 

This  is  the  winged  horse  which  sprang  from  the  blood  of  Medusa, 
after  Perseus  had  cut  off  her  head.  He  fixed  his  residence  on  Mt. 
Helicon,  where  he  was  the  favorite  of  the  Muses,  and  after  being 
tamed  by  Minerva  he  was  given  to  Bellerophon  to  aid  him  in  conquer- 
ing the  Chimsera.  After  the  destruction  of  the  monster,  Bellerophon 
attempted  to  ascend  to  heaven  upon  Pegasus,  but  the  horse  threw  off 
his  rider,  and  continued  his  flight  to  the  stars. 

78.  Aquarins,   the  Water-bearer   (Map  IV.).      October.  — 
This,   the   twelfth   and  last   of    the   zodiacal    constellations, 
extends  more  than  3^h  in   right  ascension,  covering  a  con- 
siderable region  which  by  rights  ought  to  belong  to  Capri- 
cornus.     The  most  notable  configuration  is  the  little  Y  of 
third  and  fourth  magnitude  stars  which  marks   the    "water- 
jar"  from  which  Aquarius  pours  the  stream  that  meanders 
down  to  the  southeast  and  south  for  30°,  till  it  reaches  the 
Southern  Fish.     The  middle  of  the  Y  is  about  18°  south  and 


§  78]  PISCIS   AUSTRINUS.  53 

west  of  Alpha  Pegasi,  and  lies  almost  exactly  on  the  celestial 
equator. 

Zeta,  the  central  star  of  the  Y,  is  a  pretty  and  interesting  double 
star,  distance  about  4".  The  green  nebula,  nearly  on  the  line  from 
Alpha  through  Beta,  produced  about  its  own  length,  1£°  west  of  Nu, 
is  a  planetary  nebula,  and  curious  from  the  vividness  of  its  color  (see 
map). 

There  are  various  opinions  respecting  the  origin  of  this  constella- 
tion. According  to  a  Greek  legend  it  represents  Deucalion,  the  hero 
of  the  Greek  Deluge ;  but  among  the  Egyptians  it  evidently  had  refer- 
ence to  the  rising  and  falling  of  the  Nile. 

79.  Piscis  Austrinus  (or  Australis),  the  Southern  Fish  (Map 
IV.).  October.  —  This  small  constellation,  lying  south  of  Cap- 
ricornus  and  Aquarius  in  the  stream  that  issues  from  the 
Water-bearer's  urn,  presents  little  of  interest.  It  has  one 
bright  star,  Fomalhaut  (pronounced  Fomalo),  of  the  1|-  mag- 
nitude, which  is  easily  recognized  from  its  being  nearly  on  the 
same  hour-circle  with  the  western  edge  of  the  great  square  of 
Pegasus,  45°  to  the  south  of  Alpha  Pegasi,  and  solitary,  hav- 
ing no  star  exceeding  the  fourth  magnitude  within  15°  or  20°. 

This  constellation  is  by  some  said  to  represent  the  transformation 
of  Venus  into  a  fish,  when  fleeing  from  Typhon  (but  see  Pisces). 

South  of  the  Southern  Fish,  barely  rising  above  the  southern  hori- 
zon, lie  the  constellations  of  Microscopium  and  Grus.  The  former  is 
of  no  account.  In  the  southern  hemisphere  Grus  is  a  conspicuous 
constellation,  and  its  two  brightest  stars,  Alpha  and  Beta,  of  the  sec- 
ond magnitude,  rise  high  enough  to  be  seen  in  latitudes  south  of 
Washington.  They  lie  about  20°  south  and  west  of  Fomalhaut. 


54 


URANOGRAPHY. 


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80] 


LATITUDE   DEFINED. 


55 


CHAPTER   III. 


LATITUDE,  AND  THE  ASPECT  OF  THE  CELESTIAL  SPHERE. 
—  TIME. — LONGITUDE.  —  THE  PLACE  OF  A  HEAVENLY 
BODY. 

80.  Latitude  defined,  —  In  geography  the  latitude  of  a  place 
is  usually  defined  simply  as  its  distance  north  or  south  of  the 
equator,  measured  in  degrees.  This  is  not  explicit  enough, 
unless  it  is  stated  how  the  degrees  themselves  are  to  be  meas- 
ured. There  would  be  no  difficulty  if  the  earth  were  a  perfect 
sphere ;  but  since  the  earth  is  a  little  flattened  at  the  poles, 
the  degrees  (geographical)  are  of  somewhat  different  lengths 
at  different  parts  of  the  earth.  The  exact  definition  of  the 
astronomical  latitude  of 
a  place  is  the  angle  be- 
tween the  direction  of  the 
observer's  plumb-line  and 
the  plane  of  the  earths 
equator ;  and  this  is  the 
same  as  the  altitude  of 
the  pole,  as  will  be  clear 
from  Fig.  6.  Here  the 
angle  ONQ  is  the  lati- 
tude as  defined.  If  now 
at  0  we  draw  HH1  per- 
pendicular to  OZ,  it  will 
be  a  level  line,  and  will  point  to  the  horizon.  From  0  also 
draw  OP",  parallel  to  OP',  the  earth's  axis.  Since  OP'  and 
OP"  are  parallel  they  will  be  directed  apparently  to  the  same 
point  in  the  celestial  sphere  (Art.  6),  and  this  point  is  the 


FIG.  6.  —  Relation  of  Latitude  to  the  Elevation 
of  the  Pole. 


56  MEASURING   THE   LATITUDE.  [§  80 

celestial  pole.  The  angle  H'OP"  is  therefore  the  altitude  of 
the  pole,  as  seen  at  0,  and  it  obviously  equals  ONQ ;  and  this 
is  true  whether  the  earth  be  a  sphere,  or  whatever  its  form. 
This  fundamental  relation,  THAT  THE  ALTITUDE  OF  THE  POLE 

IS    IDENTICAL    WITH    THE    OBSERVER'S    LATITUDE,  Cannot  be  tOO 

strongly  impressed  on  the  mind. 

81.  Method  of  measuring  the  Latitude.  —  The  most  obvious 
method  is  to  observe,  with  a  suitable  instrument,  the  altitude 
of  some  star  near  the  pole   (a  "  circumpolar "   star)   at  the 
moment  when  it  is  crossing  the  meridian  above  the  pole,  and 
again  twelve  hours  later,  when  it  is  once  more  on  the  meridian 
below  the  pole.    In  the  first  position,  its  elevation  is  the  great- 
est possible  j  in  the  second,  the  least.    The  average  of  these  two 
altitudes,  when  corrected  for  refraction,  is  the  latitude  of  the 
observer.     It  is  exceedingly  important  that  the  student  under- 
stand this  simple  method  of  determining  the  latitude. 

The  instrument  ordinarily  used  for  making  observations  of  this 
kind  at  an  observatory  is  called  a  meridian  circle,  and  a  brief  descrip- 
tion is  given  in  the  Appendix  (see  Art.  418). 

82.  Refraction.  —  When  we  observe  the  altitude  of  a  heav- 
enly body  with  any  instrument,  we  do  not  find  it  as  it  would 
be  if  our  atmosphere  had  no  effect  upon  the  rays  of  light.     As 
these  rays  enter  the  earth's  atmosphere  they  are  bent  down- 
ward by   "refraction/7   excepting   only   such  as  come   from 
exactly  overhead.     Since  the  observer  sees  the  object  in  the 
direction  in  which  the  rays  enter  the  eye,  without  any  reference 
to  its  real  position,  this  bending  down  of  the  rays  causes  every 
object  seen  through  the  air  to  look  higher  up  in  the  sky  than 
it  would  be  if  the  air  were  absent;   and  we  must  therefore 
correct  the   observed   altitude   by   diminishing  it  a    certain 
amount.      Under   ordinary   conditions,   refraction   elevates  a 
body  at  the  horizon  about  35',  so  that  the  sun  and  moon  in 
rising  appear  clear  of  the  horizon  while  they  are  still  wholly 


§  82]  THE   BIGHT    SPHERE.  57 

below  it.  The  refraction  correction  diminishes  very  rapidly 
as  the  body  rises.  At  an  altitude  of  only  5°  the  refraction  is 
but  10';  at  44°,  it  is  about  1';  and  at  the  zenith,  zero,  of 
course. 

Its  amount  at  any  given  time  is  affected  quite  sensibly,  however,  by 
the  temperature  and  by  the  height  of  the  barometer,  increasing  as  the 
thermometer  falls  or  as  the  barometer  rises ;  so  that  whenever  great 
accuracy  is  required  in  measures  of  altitude  we  must  have  observa- 
tions of  both  the  barometer  and  thermometer  to  go  with  the  reading 
of  the  circle.  In  works  on  Practical  Astronomy  tables  are  given  by 
which  the  refraction  can  be  computed  for  an  object  at  any  altitude 
and  in  any  state  of  the  weather.  It  is  hardly  necessary  to  say  that 
this  indispensable  correction  is  very  troublesome,  and  always  involves 
more  or  less  error. 

For  other  methods  of  determining  the  latitude,  see  Appendix, 
Art.  424. 

83.  Effect  of  the  Observer's  Latitude  upon  the  Aspect  of  the 
Heavens ;  the  Eight  Sphere.  —  If  the  observer  is  situated  at  the 
earth's  equator,  —  i.e.,  in  latitude  zero, — the  celestial  poles  will 
evidently  be  on  the  horizon,  and  the  celestial  equator  will  pass 
through  the  zenith  and  coincide  with  the  prime  vertical  (Art. 
11).     At  the  earth's  equator,  therefore,  all  heavenly  bodies 
will  rise  and  set  vertically,  and  their  diurnal  circles  will  be 
equally  divided  by  the  horizon,  so  that  they  will  be  twelve 
hours  above  it  and  twelve  hours  below  it,  and  the  length  of 
the  night  will  always  equal  that  of  the  day.     This  aspect  of 
the  heavens  is  called  the  right  sphere. 

84.  Parallel  Sphere.  —  If  the  observer  is  at  one  of  the  poles 
of  the  earth,  where  the  latitude  equals  90°,  then  the  corre- 
sponding celestial   pole   will  be   exactly   overhead,   and  the 
celestial  equator  will  coincide  with  the  horizon.     If  he  is  at 
the  north  pole,  all  the  stars  north  of  the  celestial  equator  will 
remain  permanently  visible,  never  rising  or  setting,  but  sailing 
around  the  sky  on  parallels  of  altitude,  while  the  stars  south 


58 


THE   OBLIQUE   SPHERE. 


[§84 


K 


of  the  equator  will  never  rise  to  view.  Since  the  sun  and  the 
moon  move  in  such  a  way  that  during  half  the  time  they  are 
north  of  the  equator  and  half  the  time  south  of  it,  they  will 
therefore  be  half  the  time  above  the  horizon  and  half  the  time 
below  it  (that  is,  approximately,  since  refraction  has  a  notice- 
able effect).  The  moon  will  be  visible  for  about  a  fortnight 
at  a  time,  and  the  sun  for  about  six  months. 

85.   The  Oblique  Sphere.  —  At  any  station  between  the  pole 
and  the  equator  the  pole  will  be  elevated  above  the  horizon, 

and  the  stars  will  rise  and 
set  in  oblique  circles,  as 
shown  in  Fig.  7.  Those 
stars  whose  distance  from 
the  elevated  pole  is  less 
than  PN,  the  latitude  of 
the  observer,  will  never 
set,  the  radius  of  this  "  cir- 
cle of  perpetual  appari- 
tion" being  just  equal  to 
the  height  of  the  pole,  and 
becoming  larger  as  the  lat- 
itude increases.  On  the 
other  hand,  stars  within 
the  same  distance  of  the 


FIG.  7. —The  Oblique  Sphere. 


depressed  pole  will  lie  within  the  "  circle  of  perpetual  occulta- 
tion,"  and  will  never  rise  above  the  observer's  horizon.  An 
object  which  is  exactly  on  the  celestial  equator  will  have  its 
diurnal  circle,  EQWQ',  equally  divided  by  the  horizon,  and 
will  be  above  the  horizon  just  as  long  as  below  it. 

For  an  observer  in  the  United  States,  a  star  north  of  the 
equator  will  have  more  than  half  of  its  diurnal  circle  above  the 
horizon,  and  will  be  visible  for  more  than  twelve  hours  of  each 
day;  as,  for  instance,  the  star  at  A.  Whenever  the  sun  is 
north  of  the  celestial  equator,  the  day  will  therefore  be  longer 


§  85]  THE   OBLIQUE   SPHERE.  59 

than  the  night  for  all  stations  in  northern  latitude :  how 
much  longer  will  depend  both  on  the  latitude  of  the  place  and 
the  sun's  distance  from  the  equator  (its  declination). 

86.  Moreover,  when  the  sun  is  north  of  the  equator,  it  will, 
in  the  northern  latitudes,  rise  at  a  point  north  of  east,  as  at  ~B 
in  the  figure,  and  will  continue  to  shine  on  the  north  side  of 
every  wall  that  runs  east  and  west  until,  as  it  ascends,  it 
crosses  the  prime  vertical,  EZW,  at  some  point,  as  V.     In  the 
latitude  of  New  York  the  sun  in  June  is  south  of  the  prime 
vertical  for  only  about  six  hours  of  the  whole  fifteen  during 
which  it  is  above  the  horizon.     During  nine  hours  of  the  day, 
therefore,  it  shines  into  north  windows. 

If  the  latitude  of  the  observer  is  such  that  PN,  in  the  figure, 
is  greater  than  the  sun's  polar  distance  at  the  time  when  it  is 
farthest  north,  the  sun  at  midsummer  will  make  a  complete 
circuit  of  the  heavens  without  setting,  thus  producing  the 
phenomenon  of  the  "  midnight  sun,"  visible  at  the  North  Cape 
and  at  all  stations  within  the  Arctic  Circle. 

87.  A  celestial  globe  will  be  of  great  use  in  studying  these 
diurnal   phenomena.     The  north  pole  of  the  globe  must  be 
elevated  to  an  angle  equal  to  the  latitude  of  the  observer, 
which  can  be  done  by  means  of  the  degrees  marked  on  the 
metal  meridian  ring.     It  will  then  be  seen  at  once  what  stars 
never  set,  which  ones  never  rise,  and  during  what  part  of  the 
twenty-four  hours  any  heavenly  body  at  a  known  distance 
from  the  equator  is  above  or  below  the  horizon.     For  descrip- 
tion of  the  celestial  globe,  see  Appendix,  Art.  400. 

TIME. 

Time  is  usually  denned  as  "  measured  duration,"  and  the 
standard  unit  of  time  has  always  been  obtained  in  some  way 
from  the  length  of  the  day. 


60  SOLAE   TIME.  [§88 

88.  Apparent   Solar  Time.  —  The  most  natural  way,  since 
we  are  obliged  to  regulate  our  lives  by  the  sun,  is  to  reckon 
time  by  him ;  i.e.,  to  call  it  noon  when  the  sun  is  on  the  merid- 
ian and  highest,  and  to  divide  the  day  from  one  noon  to 
another   into   its   hours,   minutes,   and   seconds.     Time   thus 
reckoned  is  called   apparent  solar  time  (see  Appendix,  Art. 
422),  which  is  the  time  shown  by  a  correctly  adjusted  sun- 
dial.    But   because  the  sun's  eastward  motion  in  the  sky  is 
not  uniform  (owing  to  the  oval  form  of  the  earth's  orbit,  and 
its  inclination  to  the  equator),  these  apparent  solar  days  are  not 
exactly  of  the  same  length.     Thus,  for  instance,  the  interval 
from  noon  of  Dec.  22d  to  noon  of  Dec.  23d  is  nearly  a  minute 
longer  than  the  interval  between  the  noons  of  Sept.  15th  and 
16th.     As  a  consequence,  it  is  only  by  very  complicated  and 
expensive  machinery  that  a  watch  or  clock  can  be  made  to 
keep  time  precisely  with  the  sundial,  and  the  attempt  was 
long  ago  given  up.     Apparent  solar  time  is  now  used  only  in 
communities  where  clocks  and  watches  are  rare,  and  sundials 
are  the  usual  timepieces. 

89.  Mean  Solar  Time.  —  At  present,  for  civil  and  business 
purposes,  time  is  almost  universally  reckoned  in  days  all  of 
which  have  precisely  the  same  length,  and  are  just  equal  to 
the  average  apparent  solar  day ;   and  this  time,  called  mean 
solar  time  (Appendix,  Art.  422),  is  that  which  is  kept  by  all 
good  timepieces. 

Sundial  time  agrees  with  mean  time  four  times  a  year;  viz.,  upon 
April  15th,  June  14th,  Sept.  1st,  and  Dec.  24th.  The  greatest  differ- 
ences occur  on  Nov.  2d  and  Feb.  llth,  when  the  sundial  is  respec- 
tively 16m  20"  fast  of  the  clock  and  14m  30s  slow.  During  the  summer 
the  difference  never  exceeds  6m.  This  difference  is  called  the  Equation 
of  Time,  and  is  given  in  the  almanac  for  every  day  in  the  year. 

90.  The  Civil  Day  and  the  Astronomical  Day.  — The  astro- 
nomical day  begins  at  noon ;  the  civil  day  at  midnight,  twelve  hours 
earlier.     Astronomical  mean  time  is  reckoned  around  through  the 


§90]  SIDEREAL  TIME.  61 

whole  twenty-four  hours,  instead  of  being  counted  in  two  series  of 
twelve  hours  each.  Thus  8  A.M.  of  Tuesday,  Aug.  12th,  civil  reck- 
oning, is  Monday,  Aug.  llth,  20h,  astronomical  reckoning.  Beginners 
need  to  bear  this  in  mind  in  referring  to  the  almanac. 

91.  Sidereal  Time,  or  Time  reckoned  by  the  Stars.  —  As  has 
been  said  (Art.  17),  the  sun  is  not  fixed  on  the  celestial  sphere, 
but  appears  to  creep  completely  around  it  once  a  year.  The 
interval  from  noon  to  noon  does  not  therefore  correspond  to 
the  true  diurnal  revolution  of  the  heavens.  If  we  reckoned  by 
the  interval  between  two  successive  passages  of  any  given 
star  across  the  .observer's  meridian,  we  should  find  that  the 
true  day,  the  sidereal  day,  as  it  is  called,  is  nearly  4m  shorter 
(3m  568.9)  than  the  ordinary  solar  day,  the  relation  being  such 
that  in  a  year  the  number  of  sidereal  days  exceeds  that  of  solar 
by  exactly  one.  For  many  purposes,  astronomers  find  it  much 
more  convenient  to  reckon  by  the  stars  than  by  the  sun. 
They  count  the  time,  however,  not  by  any  real  star,  but  from 
the  Vernal  Equinox^  the  sidereal  clock  being  so  set  and  regu- 
lated that  it  always  shows  zero  hours,  minutes,  and  seconds, 
at  the  moment  when  the  Vernal  Equinox  is  on  the  meridian 
(see  Appendix,  Art.  422).  This  kind  of  time,  of  course,  would 
not  answer  for  business  purposes,  since  its  noon  comes  at  all 
hours  of  the  day  and  night  at  different  seasons  of  the  year. 
The  almanac  gives  data  by  which  sidereal  time  and  mean  solar 
time  can  be  easily  converted  into  each  other. 

92.  The  Determination  of  Time.  —  In  practice,  the  problem 
always  takes  the  shape  of  finding  the  error  of  a  timepiece  of 
some  sort;  i.e.,  ascertaining  how  many  seconds  it  is  fast  or 
slow.  The  instrument  now  ordinarily  used  for  the  purpose  is 
the  transit  instrument,  which  is  a  small  telescope  mounted  on 
an  axis,  placed  exactly  east  and  west,  and  level,  so  that  as  the 
telescope  is  turned  it  will  follow  the  meridian ;  at  least,  the 
middle  cross-wire  in  the  field  of  view  will  do  so.  It  is  the 


62  TIME  FROM  THE   STARS.  [§  92 

same  as  the  meridian  circle,  except  that  it  does  not  require 
the  costly  graduated  circle  with  its  appendages.  For  descrip- 
tion, see  Appendix,  Art.  416. 

To  determine  with  the  transit  the  error  of  the  sidereal  clock 
which  is  ordinarily  used  in  connection  with  it,  it  is  only  neces- 
sary to  observe  the  exact  time  indicated  by  the  clock  when 
some  star  whose  right  ascension  is  known  passes,  or  "tran- 
sits," the  middle  wire  of  the  instrument. 

93.  The  right  ascension  of  a  star  (Art.  18)  is  the  number  of 
'  hours '  of  arc  (measured  along  the  equator)  by  which  the  star 
is  east  of  the  vernal  equinox ;  and  therefore  when  the  star  is 
on  the  meridian,  the  right  ascension  also  equals  the  number 
of  hours,  minutes,  and  seconds  since  the  transit  of  the  vernal 
equinox.  In  other  words,  we  may  say  that  the  right  ascension 
of  a  star  is  the  sidereal  time  at  the  moment  of  its  meridian  tran- 
sit. (This  is  often  called  the  observatory  definition  of  right 
ascension.)  For  instance,  the  right  ascension  of  Vega  (Alpha 
Lyrse)  is  18h  33m.  If  we  observe  its  transit  to  occur  at  18h  40m 
by  the  clock,  the  clock  is  obviously  7m  fast. 

With  a  good  instrument,  a  skilled  observer  can  thus  deter- 
mine the  clock-error  within  about  -^  of  a  second  of  time. 

To  get  solar  time,  we  may  observe  the  sun  itself,  the  moment 
of  its  transit  being  '  apparent  noon/  But  it  is  better,  and  it 
is  usual,  to  get  the  sidereal  time  first,  and  to  deduce  from  that 
the  solar  time  by  means  of  the  necessary  data  which  are  fur- 
nished in  the  almanac. 

The  method  by  the  transit  instrument  is  most  used,  and  is,  on  the 
whole,  the  most  convenient ;  but  since  the  instrument  requires  to  be 
mounted  upon  a  firm  pier,  it  is  not  always  available.  When  not,  we 
use  some  one  of  various  other  methods,  for  which  reference  must  be 
made  to  the  General  Astronomy.  At  sea,  and  by  travellers  on  scien- 
tific expeditions,  the  time  is  usually  determined  by  observing  the  alti- 
tude of  the  sun  with  a  sextant  some  hours  before  or  after  noon.  (See 
Appendix,  Art.  427.) 


§  94]  DETEKMINAT10N   OF  LONGITUDE.  63 

LONGITUDE. 

94.  The  problem  of  finding  the  longitude  is  in  many  respects 
the  most  important  of  what  may  be  called  the  "economic" 
problems  of  astronomy ;  i.e.,  those  of  business  utility  to  man- 
kind.    The  great  observatories  of  Greenwich  and  Paris  were 
founded  for  the  express  purpose  of  furnishing  the  necessary 
data  to  enable  the  sailor  to  determine  his  longitude  at  sea; 
and  the  English  government  has  given  great  prizes  for  the 
construction  of  clocks  and  chronometers  fit  to  be  used  in  such 
determinations. 

The  longitude  of  a  place  on  the  earth  is  defined  as  the 
arc  of  the  equator  intercepted  between  the  meridian  which  passes 
through  the  place  and  some  meridian  which  is  taken  as  the 
standard.1 

Now  since  the  earth  turns  on  its  axis  at  a  uniform  rate,  this 
arc  is  strictly  proportional  to,  and  may  be  measured  by,  the 
time  intervening  between  the  transits  of  any  given  star  across 
the  two  meridians.  The  longitude  of  a  place  may  therefore 
be  defined  as  the  amount  by  which  the  time  at  Greenwich  is  ear- 
lier or  later  than  the  time  at  the  station  of  the  observer,  and  this 
whether  we  reckon  by  solar  or  by  sidereal  time.  Accordingly, 
terrestrial  longitude  is'  usually  reckoned  in  hours,  minutes, 
and  seconds,  rather  than  in  degrees.  Since  the  observer  can 
easily  find  his  own  local  time  by  the  transit  instrument,  or  by 
some  of  the  many  other  methods,  the  knot  of  the  problem  is 
simply  this  :  To  find  the  Greenwich  time  at  any  moment  with- 
out going  to  Greenwich ;  then  we  get  the  longitude  at  once  by 
simply  comparing  it  with  our  own  time. 

95.  Methods  of  determining  Longitude.  —  Incomparably  the 
best  method,  whenever  it  is  available,  is  to  make  a  direct  tele- 

1  As  to  the  standard  meridian,  there  is  a  variation  of  usage  among  dif- 
ferent nations.  The  French  reckon  from*  the  meridian  of  Paris,  but  most 
other  nations  use  the  meridian  of  Greenwich,  at  least  at  sea. 


64  LOCAL  AND   STANDARD  TIME.  C§  95 

graphic  comparison  between  the  clock  of  the  observer  and  that 
of  some  station,  the  longitude  of  which  is  known.  The  differ- 
ence between  the  two  clocks,  duly  corrected  for  their  '  errors ' 
(Art.  92),  will  be  the  true  difference  of  longitude.  The  astro- 
nomical difference  of  longitude  between  the  two  places  can 
thus  be  determined  by  four  or  five  nights7  observations  within 
about  Os.01  —  i.e.,  within  ten  feet  or  so,  in  the  latitude  of  the 
United  States.  In  many  cases  the  telegraphic  method,  how- 
ever, is  not  available ;  never  at  sea,  of  course. 

96.  A  second  method  is  to   use   a  chronometer,  which  is 
simply  a  very  accurate  watch.     This  is  set  to  Greenwich  time 
at  some  place  whose  longitude  is  known,  and  afterwards  is 
supposed  to  keep  that  time  wherever  carried.     The  observer 
has  only  to  compare  his  own  local  time,  determined  with  the 
transit  instrument  or  sextant,  with  the  time  shown  by  such  a 
chronometer,  and  the  difference  is  his  longitude  from  Green- 
wich. 

Practically,  of  course,  no  chronometer  goes  absolutely  without  gain- 
ing or  losing ;  hence,  it  is  always  necessary  to  know  and  to  allow  for 
its  gain  or  loss  since  the  time  it  was  last  set.  Moreover,  it  is  never 
safe  to  trust  a  single  chronometer,  because  of  the  liability  of  such  in- 
struments to  change  their  rate  in  transportation.  A  number  should 
be  used,  if  possible. 

Before  the  days  of  telegraphs  and  chronometers,  astronomers 
were  generally  obliged  to  get  their  Greenwich  time  from  the 
moon,  which  may  be  regarded  as  a  clock-hand  with  the  stars 
for  dial  figures ;  but  observations  of  this  kind  are  troublesome, 
and  the  results  inaccurate,  as  compared  with  those  obtained 
by  the  telegraph  and  chronometer.  (For  further  details,  see 
General  Astronomy,  Arts.  109-116.) 

97.  Local  and  Standard  Time.  —  Until  recently  it  has  been 
always  customary  to  use  local  time,  each  station  determining 
its  own  time  by  its  own  observations,  and  having,  therefore, 


§  97]  WHERE  THE  DAY  BEGINS.  65 

a  time  differing  from  that  of  all  other  stations  not  on  the  same 
meridian.  Before  the  days  of  the  telegraph,  and  while  travel- 
ling was  comparatively  slow,  this  was  best.  At  present  there 
are  many  reasons  why  it  is  better  to  give  up  the  old  system  in 
favor  of  a  system  of  standard  time.  The  change  greatly  facil- 
itates all  railway  and  telegraphic  business,  and  makes  it  prac- 
tically easy  for  everybody  to  have  accurate  time,  since  the 
standard  time  can  be  daily  wired  from  some  headquarters  to 
every  telegraph  office. 

According  to  the  system  now  established  in  North  America, 
there  are  five  such  standard  times  in  use, — the  colonial,  the 
eastern,  the  central,  the  mountain,  and  the  Pacific,  —  which 
differ  from  Greenwich  time  by  exactly  four,  five,  six,  seven, 
and  eight  hours  respectively,  the  minutes  and  seconds  being 
everywhere  identical,  and  the  same  with  those  of  the  clock  at 
Greenwich.  In  order  to  determine  the  standard  time  by  obser- 
vation, it  is  only  necessary  to  find  the  local  time  by  one  of  the 
methods  given,  and  correct  it  according  to  the  observer's  longi- 
tude from  Greenwich. 

98.  Where  the  Day  begins.  —  It  is  clear  that  if  a  traveller 
were  to  start  from  Greenwich  on  Monday  noon,  and  travel 
westward  as  fast  as  the  earth  turns  to  the  east  beneath  his 
feet,  he  would  have  the  sun  upon  the  meridian  all  day  long, 
and  it  would  be  continual  noon.  But  what  noon  ?  It  was 
Monday  when  he  started,  and  when  he  gets  back  to  London 
twenty-four  hours  later  it  will  be  Tuesday  noon  there,  and  yet 
he  has  had  no  intervening  night.  When  did  Monday  noon 
become  Tuesday  noon  ? 

It  is  agreed  among  mariners  to  make  the  change  of  date  at 
the  180th  meridian  from  Greenwich.  Ships  crossing  this  line 
from  the  east  skip  one  day  in  so  doing.  If  it  is  Monday  after- 
noon when  a  ship  reaches  the  line,  it  becomes  Tuesday  after- 
noon the  moment  she  passes  it,  the  intervening  twenty-four 
hours  being  dropped  from  the  reckoning  on  the  log-book. 


66  POSITION  OF  A  HEAVENLY  BODY.  [§98 

Vice  versa,  when  a  vessel  crosses  the  line  from  the  western 
side,  it  counts  the  same  day  twice,  passing  from  Tuesday  back 
to  Monday. 

This  180th  meridian  passes  mainly  over  the  ocean,  hardly  touching 
land  anywhere.  There  is  some  irregularity  as  to  the  date  actually 
used  on  the  different  islands  of  the  Pacific.  Those  which  received 
their  earliest  European  inhabitants  via  the  Cape  of  Good  Hope,  have, 
for  the  most  part,  adopted  the  Asiatic  date,  even  if  they  really  lie  east 
of  the  180th  meridian,  while  those  which  were  first  approached  via 
Cape  Horn  have  the  American  date.  When  Alaska  was  transferred 
from  Russia  to  the  United  States,  it  was  necessary  to  drop  one  day  of 
the  week  from  the  official  dates. 


DETERMINATION  OF  THE  POSITION  OF  A  HEAVENLY 
BODY. 

As  the  basis  of  our  investigations  in  regard  to  the  motions 
of  the  heavenly  bodies,  we  require  a  knowledge  of  their 
places  in  the  sky  at  known  times.  By  the  "  place  "  of  a  body, 
we  mean  its  right  ascension  and  declination. 

99.  By  the  Meridian  Circle  (see  Appendix,  Art.  418).  —  If  a 
body  is  bright  enough  to  be  seen  by  the  telescope  of  the  merid- 
ian circle,  and  comes  to  the  meridian  in  the  night-time,  its 
right  ascension  and  declination  are  best  determined  by  that 
instrument.     If  the  instrument  is  in  exact  adjustment,  the 
right  ascension  of  the  body  is  simply  the  sidereal  time  when  it 
crosses  the  middle  vertical  wire  of  the  reticle.     The  'circle- 
reading/  on  the  other  hand,  corrected  for  refraction,  gives  the 
declination.     A  single  complete  observation  with  the  meridian 
circle  determines  accurately  both  the  right  ascension  and  the 
declination  of  the  object. 

100.  By  the  Equatorial. — If  the  body — a  comet,  for  instance 
—  is  too  faint  to  be  observed  by  the  telescope  of  the  meridian 
circle,  seldom  very  powerful,  or  comes  to  the  meridian  only  in 


§  100]  DETERMINATION   OF    POSITION.  67 

the  daytime,  we  usually  accomplish  our  object  by  using  the 
equatorial  (Appendix,  Art.  414),  and  determine  the  position 
of  the  body  by  measuring  with  some  kind  of  '  micrometer ? 
the  difference  of  right  ascension  and  declination  between  it 
and  a  neighboring  star  whose  place  is  given  in  some  star- 
catalogue. 


d 


.    i 


68  THE  EARTH.  [§  101 


CHAPTER  IV. 

THE  EARTH:  ITS  FORM  AND  DIMENSIONS;  ITS  ROTATION, 
MASS,  AND  DENSITY;  ITS  ORBITAL  MOTION  AND  THE 

SEASONS.  —  PRECESSION.  —  THE    YEAR    AND    THE    CAL- 
ENDAR. 

101,  In  a  science  which  deals  with  the  '  heavenly  bodies/ 
there  might  seeni  at  first  no  place  for  the  Earth.     But  certain 
facts  relating  to  the  Earth,  just  such  as  we  have  to  investi- 
gate with  respect  to  her  sister  planets,  are  ascertained  by  astro- 
nomical methods,  and  a  knowledge  of  them  is  essential  as  a 
base  of  operations.     In  fact,  Astronomy,  like  charity,  "begins 
at  home,"  and  it  is  impossible  to  go  far  in  the  study  of  the 
bodies  which  are  strictly  "  heavenly  "  until  we  have  first  ac- 
quired some  accurate  knowledge  of  the  dimensions  and  motions 
of  the  Earth  itself. 

102.  The    astronomical    facts    relating   to   the    Earth   are 
broadly  these :  — 

1.  The  earth  is  a  great  ball  about  7920  miles  in  diameter. 

2.  It   rotates  on  its  axis  once  in  twenty-four   "sidereal" 
hours. 

3.  It  is  not  exactly  spherical,  but  is  slightly  flattened  at  the 
poles ;  the  polar  diameter  being  nearly  twenty-seven  miles,  or 
•^  part  less  than  the  equatorial. 

4.  It  has  a  mean  density  of  about  5.6  times  that  of  water, 
and  a  mass  represented  in  tons  by  6  with  twenty-one  ciphers 
following,  (six  thousand  millions  of  millions  of   millions  of 
tons.) 

5.  It  is  flying  through  space  in  its  orbital  motion  around 
the  sun,  with  a  velocity  of  about  eighteen  and  a  half  miles  a 


§  102]  THE  EARTH'S  FORM  AND  SIZE.  69 

second;  i.e.,  about  seventy-five  times  as  swiftly  as  an  ordinary 
cannon-ball. 

103.  The  Earth's  Approximate  Form  and  Size.  —  It  is  not 

necessary  to  dwell  on  the  ordinary  proofs  of  the  earth's  globu- 
larity.     We  simply  mention  them. 

1.  It  can  be  sailed  around. 

2.  The  appearance  of  vessels  coming  in  from  the  sea  indi- 
cates that  the  surface  is  everywhere  convex. 

3.  The  fact  that  as  one  goes  from  the  equator  towards  the 
north  the  elevation  of  the  pole  increases  in  proportion  to  the 
distance  from  the  equator,  proves  the  same  thing. 

4.  The  outline  of  the  earth's  shadow,  as  seen  upon  the  moon 
during  lunar  eclipses,  is  such  as  only  a  sphere  could  cast. 

We  may  add,  as  to  the  smoothness  and  roundness  of  the 
earth,  that  if  the  earth  be  represented  by  an  eighteen-inch 
globe,  the  difference  between  its  greatest  and  least  diameters 
would  be  only  about  one-sixteenth  of  an  inch ;  the  highest 
mountains  would  project  only  about  one-ninetieth  of  an  inch, 
and  the  average  elevation  of  continents  and  depths  of  the 
ocean  would  be  hardly  greater  than  a  film  of  varnish.  Eela- 
tively,  the  earth  is  really  much  smoother  and  rounder  than 
most  of  the  balls  in  a  bowling-alley. 

104.  One  of  the  simplest  methods  of  showing  the  curvature  of  the 
earth  is  the  following  :  — 

In  an  expanse  of  still,  shallow  water  (a  long  reach  of  canal,  for 
instance),  set  a  row  of  three  poles  about  a  mile  apart,  with  their  tops 
projecting  to  exactly  the  same  height  above  the  surface.  On  sighting 
across,  it  will  then  be  found  that  the  middle  pole  projects  about  eight 
inches  above  the  line  that  joins  the  tops  of  the  two  end  ones,  and  from 
this  a  rough  estimate  of  the  size  of  the  earth  can  be  made  (see  General 
Astronomy,  Art.  134). 

105.  Measure  of  the  Earth's  Diameter. — The  only  accurate 
method  of  measuring  the  diameter  of  the  earth  is  the  follow- 


70 


THE  EAETH'S  DIAMETER. 


[§105 


ing,  the  principle  of  which  is  very  simple,  and  should  be  thor- 
oughly mastered  by  the  student :  — 

It  consists  in  finding  the  length  in  miles  of  an  arc  of  the 
earth's  surface  containing  a  known  number  of  degrees.  From 

this  we  get  the  length  of  one  degree, 
and  this  gives  the  circumference  of 
the  earth  (since  it  contains  360°), 
and  from  this  the  diameter  is  ob- 
tained by  dividing  it  by  3.14159. 

To  do  this,  we  select  two  sta- 
tions, a  and  b  (Fig.  8),  some  hun- 
dreds of  miles  apart  on  the  same 
meridian,  and  determine  the  lati- 
tude (or  the  altitude  of  the  pole)  at 
each  station  by  astronomical  obser- 
vation. The  difference  of  latitude 
(i.e.,  ECb  —  ECa)  is  evidently  the 
number  of  degrees  in  the  arc  ab, 
and  the  determination  of  this  dif- 
ference of  latitude  is  the  only  astro- 
nomical operation  necessary. 

Next,  the  distance  in  miles  be- 
tween the  two  stations  must  be 
measured.  This  is  geodetic  work,  and  it  is  enough  for  our 
purpose  here  to  say  that  it  can  be  done  with  great  precision  by 
a  process  which  is  called  '  triangulation.' 

This  measuring  of  arcs  has  been  done  on  many  parts  of  the 
earth's  surface,  and  the  result  is  that  the  average  length  of  a 
degree  is  found  to  be  a  little  more  than  sixty-nine  miles,  and 
the  mean  diameter  of  the  earth  about  7918  miles.  The  reason 
why  we  say  average  length  and  mean  diameter  is  that  the 
earth,  as  has  been  said,  is  not  quite  a  globe,  but  is  slightly 
flattened  at  its  poles,  so  that  the  lengths  of  the  degrees  dif- 
fer in  different  parts  of  the  earth,  as  we  shall  soon  see  (Art. 
110). 


FIG.  8.  —Measuring  the  Earth's 
Diameter. 


§  106]  THE  ROTATION   OF  THE  EARTH.  71 

106.  The  Rotation  of  the  Earth.  —  Ptolemy  understood  that 
the  earth  was  round,  but  he  and  all  his  successors  deliberately 
rejected  the  theory  of  its  rotation.     Though  the  idea  that  the 
earth  might  turn  upon  an  axis  was  not  unfamiliar,  they  con- 
sidered that  there  were  conclusive  reasons  against  it.     At  the 
time  when  Copernicus  of  Thorn,  in  Poland  (1473-1543),  pro- 
posed his  theory  of  the  solar  system,  the  only  argument  he 
could  urge  in  favor  of  the  earth's  rotation1  was   that  this 
hypothesis  was  much  more  probable  than  the  older  one  that 
the   heavens  themselves   revolve.     All  the  phenomena  then 
known  would  be  sensibly  the  same  on  either  supposition.    The 
apparent  daily  motion  of  the  heavenly  bodies  can  be  perfectly 
accounted  for  (within  the  limits  of  such  observations  as  were 
then  possible)  either  by  supposing  that  they  are  actually  at- 
tached to  the  celestial  sphere,  which  turns  daily,  or  that  the 
earth  itself  spins  upon  an  axis  once  in  twenty-four  hours ;  and 
for  a  long  time  the  latter  hypothesis  did  not  seem  to  most 
people  so  reasonable  as  the  older  and  more  obvious  one.     A 
little   later,   after  the  telescope  had  been  invented,  analogy 
could  be  appealed  to ;  for  we  can  see  with  the  telescope  that 
the  sun  and  moon  and  many  of  the  planets  really  rotate  upon 
axes.     At  present  we  can  go  still  farther,  and  can  absolutely 
demonstrate  the  earth's   rotation  by  experiments,   some  of 
which  even  make  it  visible. 

107.  Foucault's  Pendulum  Experiment.  —  Among  these  ex- 
perimental proofs,  the   most   impressive   is   the   "pendulum 
experiment"  devised  by  Foucault  in  1851.     From  the  dome 
of  the  Pantheon,  in  Paris,  he  hung  a  heavy  iron  ball  by  a 
slender  wire  more  than  200  feet  long  (Fig.  9).     A  circular  rail, 

1  The  word  rotation  denotes  a  spinning  motion,  like  that  of  a  wheel  on 
its  axis.  The  word  revolve  is  more  general,  and  may  be  used  to  describe 
such  a  spinning  motion,  or  (and  this  is  the  more  common  use  in  Astron- 
omy) to  describe  the  motion  of  a  body  travelling  around  another,  as  when 
we  say  the  earth  « revolves '  around  the  sun. 


FOUCAULT'S  PENDULUM  EXPERIMENT. 


[§107 


with  a  little  ridge  of  sand  built  upon  it,  was  placed  in  such  a 

way  that  a  pin  attached  to  the  swinging  ball  would  just  scrape 

the  sand  and  leave  a  mark  at 
each  vibration.  To  put  the 
ball  in  motion,  it  was  drawn 
aside  by  a  cotton  cord  and 
left  for  some  hours,  until 
it  came  absolutely  to  rest. 
Then  the  cord  was  burned 
off,  and  the  pendulum  started 
to  swing  in  a  true  plane. 

But  this  plane  at  once  be- 
gan to  deviate  slowly  towards 
the  right,  so  that  the  pin  on 
the  pendulum  ball  cut  the 
sand  ridge  in  a  new  place  at 
each  swing,  shifting  at  a  rate 
which  would  carry  the  line 
fully  around  in  about  thirty- 
two  hours,  if  the  pendulum 
did  not  first  come  to  rest.  In 
fact,  the  floor  was  actually 

and  visibly  turning  under  the  plane  defined  by  the  swinging 

of  the  pendulum. 

The  experiment  created  great  enthusiasm  at  the  time,  and  has  since 
been  frequently  performed.  The  pendulum  used  in  such  experiments 
must,  in  order  to  secure  success,  have  a  round  ball,  must  be  suspended 
by  a  round  wire  or  on  a  point,  and  must  be  very  heavy,  very  long,  and 
very  carefully  protected  against  currents  of  wind.  At  the  pole  the 
plane  of  the  pendulum  will  shift  completely  around  once  in  twenty- 
four  hours ;  at  the  equator,  it  will  not  turn  at  all ;  and  in  the  interme- 
diate regions,  it  will  shift  more  or  less  rapidly  according  to  the  latitude 
of  the  place  where  the  experiment  is  performed.  (For  fuller  descrip- 
tion, see  General  Astronomy,  Arts.  140,  141.) 

There  are  a  number  of  other  experimental  proofs  of  the  earth's  rota- 
tion, which  are  really  just  as  conclusive  as  the  one  above  cited.  (Gen- 
eral Astronomy,  Arts.  138-144.) 


FIG.  9.  —  Foucault's  Pendulum  Experiment. 


§  108]  THE  EARTH'S  ROTATION.  73 

108.  Invariability  of  the  Earth's  Rotation,  —  It  is  a  question 
of  great  importance  whether  the  day  ever  changes  its  length. 
Theoretically,  it  must  almost  necessarily  do  so.  The  friction 
of  the  tides  and  the  fall  of  meteors  upon  the  earth  both  tend 
to  retard  the  rotation,  while,  on  the  other  hand,  the  earth's 
loss  of  heat  by  radiation  and  the  consequent  shrinkage  of  the 
globe  must  tend  to  accelerate  it,  and  to  shorten  the  day.  Then 
geological  changes,  the  elevation  and  subsidence  of  continents, 
and  the  transportation  of  soil  by  rivers,  act,  some  one  way  and 
some  the  other.  At  present  we  can  only  say  that  the  change, 
if  any  change  has  occurred  since  Astronomy  became  accurate, 
has  been  too  small  to  be  detected.  The  day  is  certainly  not 
longer  or  shorter  by  the  y-^-g-  part  of  a  second  than  it  was  in 
the  days  of  Ptolemy;  probably  it  has  not  changed  by  the 
Part  °^  a  second,  though  of  that  we  can  hardly  be  sure. 


109.  Permanence  of  the  Earth's  Axis.  —  Another  equally  in- 
teresting question  is  whether  the  earth's  axis  is,  or  is  not,  absolutely 
fixed  in  its  position  within  the  globe.     Theoretically,  any  changes 
which  may  occur  in  the  distribution  of  matter  upon  the  surface  by 
rivers  or  ocean  currents,  for  instance,  should  displace  the  axis  more 
or  less.     But  thus  far,  until  very  recently,  the  changes,  if  real,  have 
been  too  small  for  detection.     In  1889,  however,  observers  at  several 
stations  in  Germany,  working  together,  seem  to  have  proved  that  dur- 
ing the  summer  of  that  year  a  small  displacement  of  the  north  pole, 
amounting  to  some  forty  or  fifty  feet,  actually  did  occur,  changing  the 
latitudes  of  German  observatories  by  about  0".5.     We  mention  this 
mainly  to  prevent  the  student  from  conceiving  of  the  earth's  axis  as  a 
real  rod  running  through  it,  like  the  axle  of  a  wheel.     The  axis  is 
only  an  imaginary  line,  like  the  axis  of  a  base-ball  which  spins  as  it 
flies  through  the  air.     There  is  nothing  to  prevent  the  axis  from  shift- 
ing about  within  the  earth  if  any  force  operates  sufficient  to  displace 
it. 

110.  Effect  of   the  Earth's  Rotation  on  its  Form.  —  The 

whirling  of  the  earth  on  its  axis  tends  to  make  the  globe 
bulge  at  the  equator  and  flatten  at  the  poles,  in  the  way  illus- 


74 


THE  EARTH'S  ROTATION. 


[§110 


trated  by  the  well-known  little  apparatus  shown  in  Fig.  10. 

That  the  equator  does  really  bulge  in  this  way  is  shown  by 

measuring  the  length  of  a 
degree  of  latitude  on  the  va- 
rious parts  of  the  earth's 
surface  between  the  equator 
and  the  pole,  in  the  manner 
indicated  a  few  pages  back 
(Art.  105).  More  than 
twenty  such  arcs  have  been 
measured,  and  it  appears 
that  the  length  of  the  de- 

}.  10.  — Effect  of  Earth's  Rotation  on  its  Form.  OTPP.S     increases     regularly 


from  the  equator  towards  the  poles,  as  shown  in  the  following 
table:  — 

At  the  equator,  one  degree  =  68.704  miles 


At  lat.  20° 

((       II       4.QO 

«     "     60° 

«(       «       gQO 

At  the  pole, 


=  68.786 
=  68.993 
=  69.230 


=  69.407 


The  difference  between  the  equatorial  and  polar  degree  of 
latitude  is  more  than  0.7  of  a  mile,  or  over  3700  feet,  while 
the  probable  error  of  measurement  cannot  exceed  a  foot  or 
two  to  the  degree. 

From  this  table  it  can  be  calculated,  by  methods  which 
cannot  be  explained  without  assuming  too  much  mathematical 
knowledge  in  our  readers,  that  the  earth  is  orange-shaped,  or 
"an  oblate  spheroid,"  the  diameter  from  pole  to  pole  being 
7899.74  miles,  while  the  equatorial  diameter  is  7926.61  miles. 
The  difference,  26.87  miles,  is  about  -g^-g-  of  the  equatorial 
diameter.  This  fraction,  ^i-j,  is  called  the  oblateness  or  ellip- 
ticity  of  the  earth. 

Scholars  are  often  puzzled  by  the  fact  that  although  the  pole  is 
nearer  the  centre  of  the  earth  than  the  equator,  yet  the  degrees  of  lat- 


§  H°]    SURFACE  AND  VOLUME  OF  THE  EARTH.      75 

itude  are  longest  at  the  pole.  It  is  because  the  earth's  surface  there  is 
more  nearly  flat  than  anywhere  else,  so  that  a  person  has  to  travel 
more  miles  to  change  the 
direction  of  his  plumb- 
line  one  degree.  Fig.  11 
illustrates  this.  The  an- 
gles adb  andfhg  are  equal, 
but  the  arc  ab  is  longer 
than  fg. 

111.  Effect    of   the 
Earth's    Rotation    and 

Ellipticlty       Upon       the    Fm-n-  —  Length  of  Degrees  in  Different  Latitudes. 

Force  of  Gravity.  —  For  two  reasons  the  force  of  gravity  is 
less  at  the  equator  than  at  the  poles.  (1)  The  surface  of  the 
earth  is  there  13^-  miles  farther  from  the  centre,  and  this  fact 
diminishes  the  gravity  at  the  equator  by  about  -5-^.  (2)  The 
centrifugal  force  of  the  earth's  rotation  reduces  the  gravity  at 
the  equator  by  about  -^-g- ;  the  whole  reduction,  therefore  (-3-3-5- 
-f  2-f^X  is  very  nearly  equal  to  -^ ;  i.e.,  an  object  which  weighs 
190  pounds  at  the  equator  would  weigh  191  pounds  near  the  pole, 
— weighed  by  an  accurate  spring-balance.  (In  an  ordinary  bal- 
ance, the  loss  of  weight  would  not  show,  simply  because  the 
weights  themselves  would  be  affected  as  much  as  the  body 
weighed,  so  that  the  balance  would  not  be  disturbed.)  The 
effect  of  this  variation  of  gravity  from  the  pole  to  the  equator 
is  especially  evident  in  the  going  of  a  pendulum  clock.  Such 
a  clock,  adjusted  to  keep  accurate  time  at  the  equator,  would 
gain  3m  37s  a  day  near  the  pole.  In  fact,  one  of  the  best  ways 
of  determining  the  form  of  the  earth  is  by  experiments  with  a 
pendulum  at  stations  which  differ  considerably  in  latitude. 

112.  Surface  and  Volume  of  the  Earth.  —  The  earth  is  so 
nearly  spherical  that  we  can  compute  its  surface  and  volume 
with  sufficient  accuracy  by  the  formula  for  a  perfect  sphere, 
provided  we  put  the  earth's  mean  semi-diameter  for  the  radius 


76  THE  EARTH'S  MASS  AND  DENSITY.  [§  112 

of  the  sphere.  This  mean  semi-diameter  is  not  the  average  of 
the  polar  and  equatorial  diameters,  but  is  found  by  adding  the 
polar  diameter  to  twice  the  equatorial,  and  dividing  by  three. 
It  comes  out  7917.66  miles.  From  this  we  find  the  earth's 
surface  to  be,  in  round  numbers,  197,000000  square  miles,  and 
its  volume,  or  bulk,  260000,000000  cubic  miles. 


113.  The  Earth's  Mass  and  Density.  —  The  volume  (or  bulk) 
of  a  globe  is  simply  the  number  of  cubic  miles  of  space  which 
it  contains.     If  the  earth  were  all  made  of  feathers  or  of  lead, 
its  volume  would  remain  the  same,  as  long  as  the  diameter 
was  not  altered.     The  earth's  mass,  on  the  other  hand,  is  the 
quantity  of  matter  in  it  —  the  number  of  tons  of  rock  and 
water  which  compose  it,  —  and  of  course  it  makes  a  great  dif- 
ference with   this  whether   the   material  be  heavy  or  light. 
The  density  of  the  earth  is  the  number  of  times   its   mass 
exceeds  that  of  a  sphere  of  pure   water  having  the   same 
dimensions. 

^^*^\. 

The  methods  by  which  the  mass  of  the  earth  can  be  measured 
depend  upon  a  comparison  between  the  attraction  which  the  earth 
exerts  upon  a  body  at  its  surface  and  the  attraction  which  is  exerted 
upon  the  same  body  by  another  large  body  of  known  mass  and  at  a 
known  distance.  The  experiments  are  delicate  and  difficult,  and  we 
must  refer  for  details  to  our  larger  book,  General  Astronomy,  Arts. 
164-179. 

The  most  recent  operations  of  the  kind  have  been  conducted 
at  Potsdam  in  1887-88,  and  they  show  that  the  density  of  the 
earth  is  about  5.58  times  that  of  water,  and  its  mass  in  tons 
about  6000  millions  of  millions  of  millions,  as  before  stated  in 
Art.  102. 

114.  Constitution  of  the  Earth's  Interior.  —  Since  the  average 
density  of  the  earth's  crust  does  not  exceed  three  times  that 
of  water,  while  the  mean  density  of  the  whole  earth  is  about 
5.58,  it  is  clear  that  at  the  earth's  centre  the  density  must  be 


§  114]  THE   SUN   AND   THE  EARTH.  77 

very  much,  greater  than  at  the  surface.  Very  likely  it  is  as 
high  as  eight  or  ten  times  the  density  of  water,  and  equal  to 
that  of  the  heavier  metals. 

There  is  nothing  surprising  in  this.  If  the  earth  were  once  fluid,  it 
is  natural  to  suppose  that  the  densest  materials,  in  the  process  of 
solidification,  would  settle  towards  the  centre. 

Whether  the  centre  of  the  earth  is  now  solid  or  fluid,  it  is  difficult 
to  say  with  certainty.  Certain  tidal  phenomena,  to  be  mentioned 
hereafter,  have  led  Sir  William  Thomson  to  conclude  that  the  earth  as 
a  whole  is  solid  throughout,  and  "  more  rigid  than  glass,"  volcanic  cen- 
tres being  mere  "pustules,"  so  to  speak,  in  the  general  mass.  To  this 
most  geologists  demur,  maintaining  that  at  the  depth  of  not  many 
hundred  miles  the  materials  of  the  earth  must  be  fluid,  or  at  least 
semi-fluid.  They  infer  this  from  the  phenomena  of  volcanoes,  and 
from  the  fact  that  the  temperature  continually  increases  with  the 
depth,  so  far  at  least  as  we  have  yet  been  able  to  penetrate. 

THE  APPARENT  MOTION  OF  THE  SUN  AND  THE  ORBITAL 
MOTION  OF  THE  EARTH,  AND  THEIR  IMMEDIATE  CON- 
SEQUENCES. 

115.   The  Sun's  Apparent  Motion  among  the  Stars. — The 

sun's  apparent  motion  among  the  stars,  which  makes  it  describe 
the  circuit  of  the  heavens  once  a  year,  must  have  been  among 
the  earliest  recognized  astronomical  phenomena,  as  it  is  one 
of  the  most  important.  The  sun,  starting  in  the  spring, 
mounts  northward  in  the  sky  each  day  at  noon  for  three 
months,  appears  to  stand  still  a  few  days  at  the  summer  sol- 
stice, and  then  descends  towards  the  south,  reaching  in  autumn 
the  same  noon-day  elevation  which  it  had  in  the  spring.  It 
keeps  on  its  southward  course  to  the  winter  solstice  (in  Decem- 
ber), and  then  returns  to  its  original  height  at  the  end  of  a 
year,  by  its  course  causing  and  marking  the  seasons. 

Nor  is  this  all.  The  sun's  motion  is  not  merely  north  and 
south,  but  it  also  advances  continually  eastward  among  the  stars. 
It  is  true  that  we  cannot  see  the  stars  near  the  sun  in  the 


78  THE  ECLIPTIC.  [§  115 

same  way  that  we  can  those  about  the  moon,  so  as  to  be  able 
directly  to  perceive  this  motion ;  but  in  the  spring  the  stars 
which  are  rising  in  the  eastern  horizon  are  different  from 
those  which  are  found  there  in  the  summer  or  in  the  winter. 
In  March  the  most  conspicuous  of  the  eastern  constellations 
at  sunset  are  Leo  and  Bootes.  A  little  later  Virgo  appears ;  in 
the  summer  Ophiuchus  and  Libra ;  still  later  Scorpio ;  while 
in  midwinter  Orion  and  Taurus  are  ascending  as  the  sun  goes 
down. 

So  far  as  the  obvious  appearances  are  concerned,  it  is  quite 
indifferent  whether  we  suppose  the  earth  to  revolve  around 
the  sun,  or  vice  versa.  That  the  earth  really  moves,  hoVever, 
is  absolutely  demonstrated  by  two  phenomena  too  minute  and 
delicate  for  observation  without  the  telescope,  but  accessible 
to  modern  methods.  One  of  them  is  the  aberration  of  light, 
the  other  the  annual  parallax  of  the  fixed  stars.  These  can  be 
explained  only  by  the  actual  motion  of  the  earth,  but  we  post- 
pone their  discussion  for  the  present  (see  Art.  343,  and  Appen- 
dix, 435). 

116.  The  Ecliptic ;  its  Related  Points  and  Circles.  —  By  ob- 
serving daily  with  the  meridian  circle  the  sun's  declination 
and  the  difference  between  its  right  ascension  and  that  of 
some  standard  star,  we  obtain  a  series  of  positions  of  the  sun's 
centre  which  can  be  plotted  on  the  globe,  and  we  can  thus 
mark  out  the  path  of  the  sun  among  the  stars.  It  turns  out 
to  be  a  great  circle,  as  is  shown  by  its  cutting  the  celestial  equa- 
tor at  two  points  just  180°  apart  (the  so-called  "  equinoctial 
points"  or  "equinoxes"),  where  it  makes  an  angle  with  the 
equator  of  approximately  23y  (23°  27'  14"  in  1890). 

This  great  circle  is  called  the  Ecliptic,  because,  as  was  early 
discovered,  eclipses  happen  only  when  the  moon  is  crossing 
it.  Its  position  among  the  constellations  is  shown  upon  the 
equatorial  star-maps.  It  may  be  defined  as  the  circle  in  which 
the  plane  of  the  earth's  orbit  cuts  the  celestial  sphere. 


§  116]  THE   ZODIAC.  79 

The  angle  which,  the  ecliptic  makes  with  the  equator  at  the 
equinoctial  points  is  called  the  obliquity  of  the  Ecliptic.  This 
obliquity  is  evidently  equal  to  the  sun's  greatest  distance  from 
the  equator;  i.e.,  its  maximum  declination,  which  is  reached  in 
December  and  June. 


117.  The  two  points  in  the  ecliptic  midway  between  the 
equinoxes  are  called  the  solstices,  because  at  these  points  the 
sun  "  stands  " ;  that  is,  ceases  to  move  north  or  south.     Two 
circles  drawn  through  the  solstices  parallel  to  the  equator  are 
called  the  tropics,  or  "  turning-lines,"  because  there  the  sun 
turns  from  its  northward  motion  to  the  southward,  or  vice 
versa.    The  two  points  in  the  heavens  90°  distant  from  the 
ecliptic  are  called  the  poles  of  the  ecliptic.     The  northern  one 
is  in  the  constellation  of  Draco,  about  midway  between  the 
stars  Delta  and  Zeta  Draconis,  at  a  distance  from  the  pole  of 
the  heavens  equal  to  the  obliquity  of  the  ecliptic,  or  about 
23  y,  and  on  the  Solstitial  Colure,  the  hour-circle  which  runs 
through  the  two  solstices,  the  hour-circle  which  passes  through 
the   equinoxes   being  called  the   Equinoctial  Colure.      Great 
circles  drawn  through  the  poles  of  the  ecliptic,  and  therefore 
perpendicular,  or  "  secondaries,"  to  the  ecliptic,  are  known  as 
circles  of  latitude.     It  will  be  remembered  (Art.  20)  that  celes- 
tial longitude  and  latitude  are  measured  with  reference  to  the 
ecliptic,  and  not  to  the  equator. 

118.  The  Zodiac  and  its  Signs.  — A  belt  16°  wide  (8°  on 
each  side  of  the  ecliptic)  is  called  the  Zodiac,  or  zone  of  ani- 
mals, the  constellations  in  it,  excepting  Libra,  being  all  figures 
of  animals.      It   is   taken   of  that   particular  width  simply 
because  the  moon  and  all  the  principal  planets  always  keep 
within  it.     It  is  divided  into  the  so-called  signs,  each  30°  in 
length,  having  the  following  names  and  symbols :  — 


80  THE  EARTH'S  ORBIT.  [§  us 

(  Aries       T  (  Libra  =2= 

Spring      I  Taurus     8  Autumn  <  Scorpio  nt 

(  Gemini    n  (  Sagittarius      / 

(  Cancer    05  (  Capricornus    VJ 

Summer  <  Leo          SI  Winter    <  Aquarius        ^ 

(  Virgo       Ttj?  (  Pisces  X 

The  symbols  are  for  the  most  part  conventionalized  pictures  of  the 
objects.  The  symbol  for  Aquarius  is  the  Egyptian  character  for 
water.  The  origin  of  the  signs  for  Leo,  Capricornus,  and  Virgo  is 
not  quite  clear. 

The  zodiac  is  of  extreme  antiquity.  In  the  zodiacs  of  the 
earliest  history,  the  Fishes,  Ram,  Bull,  Lion,  and  Scorpion 
appear  precisely  as  now. 

119.  The  Earth's  Orbit.  —  The  ecliptic  must  not  be  con- 
founded with  the  earth's  orbit.  It  is  simply  a  great  circle  of 
the  infinite  celestial  sphere,  —  the  trace  made  upon  that  sphere 
by  the  plane  of  the  earth's  orbit,  as  was  stated  in  its  definition. 
The  fact  that  the  ecliptic  is  a  great  circle  gives  us  no  informa- 
tion about  the  earth's  orbit  itself,  except  that  it  lies  in  one 
plane  passing  through  the  sun.  It  tells  us  nothing  as  to  the 
orbit's  real  form  and  size. 

By  reducing  the  observations  of  the  sun's  right  ascension 
and  declination  through  the  year  to  longitude  and  latitude 
(the  latitude  would  always  be  exactly  zero  except  for  some 
slight  perturbations  due  chiefly  to  the  moon's  revolution 
around  the  earth),  and  combining  these  data  with  observations 
of  the  sun's  apparent  diameter,  we  can,  however,  ascertain  the 
form  of  the  earth's  orbit  and  the  law  of  its  motion.  The  size 
of  the  earth's  orbit,  i.e.,  its  scale  of  miles,  cannot  be  fixed  until 
we  find  the  sun's  distance. 

The  result  is  that  the  orbit  is  found  to  be  very  nearly  a 
circle,  but  not  exactly  so.  It  is  an  oval  or  ellipse,  with  the  sun 
at  one  of  its  foci  (as  illustrated  in  Fig.  12),  but  is  much  more 


119] 


DEFINITION    OF   TERMS. 


81 


nearly  circular  than  the  oval  there  represented.  Its  eccen- 
tricity is  only  about  -fa  ;  that  is  to  say,  the  distance  from  the 
centre  of  the  sun  to  the  mid- 
dle of  the  ellipse  is  only  about 
J^  of  the  average  distance  of 
the  sun  from  the  earth. 

The  method  by  which  we 
proceed  to  ascertain  the  form 
of  the  orbit  may  be  found  in 
the  Appendix,  Art.  428.  For 
a  description  of  the  ellipse, 
see  Art.  429.  FlQ-  ™'-'rhe  E1IiP8e- 


120.  Definition  of  Terms.  —  The  points  where  the  earth  is 
nearest  to  and  most  remote  from  the  sun  are  called  respec- 
tively the  Perihelion  and  the  Aphelion  (Dec.  31st  and  June 
30th),  the  line  joining  them  being  the  major  axis  of  the  orbit. 
This  line,  indefinitely  produced  in  both  directions,  is  called 
the  (  Line  of  Apsides'  (pronounced  Ap'-si-deez),  the  major  axis 
being  a  limited  piece  of  it.  A  line  drawn  from  the  sun  to  the 
earth,  or  to  any  other  planet  at  any  point  in  its  orbit,  as  SP  in 
Fig.  12,  is  called  the  planet's  Radius  Vector. 

The  variations  in  the  sun's  apparent  diameter  due  to  our 
changing  distance  are  too  small  to  be  detected  without  a 
telescope,  so  that  the  ancients  failed  to  perceive  them.  Hip- 
parchus,  however,  about  120  B.C.,  discovered  that  the  earth  is 
not  in  the  centre1  of  the  circular  orbit  which  he  supposed  the 
sun  to  describe  around  it  with  uniform  velocity. 

Obviously  the  sun's  apparent  motion  is  not  uniform,  because 
it  takes  186  days  for  the  sun  to  pass  from  the  vernal  equinox, 

1  Hipparchus  (and  every  one  else  until  the  time  of  Kepler,  1607) 
assumed  on  metaphysical  grounds  that  the  sun^s  orbit  must  necessarily 
be  a  circle,  and  described  with  a  uniform  motion,  because  (they  said)  the 
circle  is  the  only  perfect  curve,  and  uniform  motion  is  the  only  perfect 
motion  proper  for  heavenly  bodies. 


82  LAW   OF   THE  EARTH'S  MOTION.  [§  120 

March  20th,  to  the  autumnal,  Sept.  22d  and  only  179  days  to 
return.  Hipparchus  explained  this  on  the  hypothesis  that  the 
earth  is  out  of  the  centre  of  the  circle. 

121.  The  Law  of  the  Earth's  Motion. — By  combining  the 
measured  apparent  diameter  of  the  sun  with  the  differences  of 
longitude  from  day  to  day,  we  can  deduce  mathematically  not 

only  the  form  of  the  earth's  or- 
bit, but  the  law  of  her  motion  in 
it.  It  can  be  shown  from  the 
comparison  that  the  earth  moves 
in  such  a  way  that  its  radius 
vector  describes  areas  proportional 
to  the  time,  a  law  which  Kepler 
first  brought  to  light  in  1609  j 
that  is  to  say,  if  ab,  cd}  ef  (Fig. 

Fio.l3.-EquableDe8criptionof  Areas.    ^  ^    portions   Qf   the   orbit  de_ 

scribed  by  the  earth  in  different  weeks,  the  areas  of  the  ellip- 
tical sectors  aSb,  cSd,  and  eSf  are  all  equal.  A  planet  near 
perihelion  moves  faster  than  at  aphelion  in  just  such  propor- 
tion as  to  preserve  this  relation. 

As  Kepler  left  the  matter,  this  is  a  mere  fact  of  observation. 
Newton  afterwards  proved  that  it  is  the  necessary  mechanical 
consequence  of  the  fact  that  the  earth  moves  under  the  action 
of  a  force  always  directed  towards  the  sun. 

It  is  true  in  every  case  of  the  elliptical  motion  of  a  heavenly  body, 
and  enables  us  to  find  the  position  of  the  earth  or  of  any  planet,  when 
we  once  know  the  time  of  its  orbital  revolution  (technically  the 
"period  "),  and  the  time  when  it  was  last  at  perihelion.  The  solution 
of  the  problem,  first  worked  out  by  Kepler,  lies,  however,  quite  beyond 
the  scope  of  the  present  work. 

122.  Changes  in  the  Earth's  Orbit.  —  The  orbit  of  the  earth 
changes  slowly  in  form  and  position,  though  in  the  long  run 
it  is  absolutely  unchangeable  as  regards   the   length  of  its 
major  axis  and  the  duration  of  the  year. 


122] 


THE  SEASONS. 


83 


These  so-called  "secular  changes"  are  due  to  "perturba- 
tions" caused  by  the  action  of  the  other  planets  upon  the 
earth.  Were  it  not  for  their  attraction  the  earth  would  keep 
her  orbit  with  reference  to  the  sun  and  stars  absolutely 
unaltered  from  age  to  age. 

Besides  these  secular  perturbations  of  the  earth's  orbit,  the 
earth  itself  is  also  continually  being  slightly  disturbed  in  its 
orbit.  On  account  of  its  connection  with  the  moon,  it  oscil- 
lates each  month  a  few  hundred  miles  above  and  below  the 
true  plane  of  the  ecliptic,  and  by  the  action  of  the  other 
planets  is  sometimes  set  backwards  or  forwards  in  its  orbit  to 
the  extent  of  some  thousands  of  miles.  Of  course  every  such 
displacement  of  the  earth  produces  a  corresponding  slight 
change  in  the  apparent  position  of  the  sun  and  of  the  nearer 
planets. 

Autumnal  Equinox 


Perihelia 


Vernal  Equinox 
FIG.  14.  — The  Seasons. 

123.  The  Seasons.  —  The  earth  in  its  motion  around  the  sun 
always  keeps  its  axis  nearly  parallel  to  itself  during  the  whole 
year,  for  the  mechanical  reason  that  a  spinning  globe  main- 


84  THE   SEASONS.  [§  123 

tains  the  direction  of  its  axis  invariable,  unless  disturbed  by 
some  outside  force  (very  prettily  illustrated  by  the  gyro- 
scope). Fig.  14  shows  the  way  in  which  the  north  pole  of 
the  earth  is  tipped  with  reference  to  the  sun  at  different 
seasons  of  the  year.  At  the  vernal  equinox  (March  20th)  the 
earth  is  situated  so  that  the  plane  of  its  equator  passes 
through  the  sun.  At  that  time,  therefore,  the  circle  which 
bounds  the  illuminated  portion  of  the  earth  passes  through 
the  two  poles,  as  shown  in  Fig.  15,  B,  and  day  and  night  are 

therefore  equal,  as  implied  by  the 
term  '  equinox.'    The  same  is  again 
true    on    the    22d    of    September. 
About  the  21st  of  June  the  earth  is 
so  situated  that  its  north  pole  is 
inclined  towards  the  sun  by  about 
FIG.  is. -Position  of  Pole  at  Solstice  23£°,  as  shown  in  Fig.  15,  A.     The 
and  Equinox.  south  pole  is  then  in  the  unlighted 

half  of  the  earth's  globe,  while  the  north  pole  receives  sunlight 
all  day  long,  and  in  all  portions  of  the  northern  hemisphere 
the  day  is  longer  than  the  night.  In  the  southern  hemi- 
sphere, on  the  other  hand,  the  reverse  is  true. 

At  the  time  of  the  winter  solstice  the  southern  pole  has  per- 
petual sunshine,  and  the  north  pole  is  in  the  night.  At  the 
equator  of  the  earth,  day  and  night  are  equal  at  all  times  of 
the  year,  and  at  that  part  of  the  earth  there  are  no  seasons  in 
the  proper  sense  of  the  word.  Everywhere  else  the  day  and 
night  are  unequal,  except  when  the  sun  is  at  one  of  the 
equinoxes. 

In  high  latitudes  the  inequality  between  the  lengths  of  the 
day  in  summer  and  in  winter  is  very  great;  and  at  places 
within  the  polar  circle  there  are  always  days  in  winter  when 
the  sun  does  not  rise  at  all,  and  others  in  the  summer  when  it 
does  not  set,  but  we  have  the  phenomenon  of  the  "  midnight 
sun,"  as  it  is  called.  At  the  pole  itself,  the  summer  is  one 
perpetual  day,  six  months  in  length,  while  the  winter  is  a  six- 
months  night. 


§  123]  EFFECTS    ON   TEMPERATURE.  85 

Perhaps  the  student  will  get  a  better  idea  by  thinking  of  the  earth 
as  a  globe  floating,  just  half  immersed,  on  a  sheet  of  still  water,  and  so 
weighted  that  its  poles  dip  at  an  angle  of  23  £°,  while  it  swims  in  a 
circle  around  the  sun,  a  much  larger  globe,  also  floating  on  the  same 
surface.  The  sheet  of  water  corresponds  to  the  ecliptic,  while  the 
plane  of  the  equator  is  a  circle  on  the  globe  itself,  drawn  square  to  the 
axis.  If,  now,  the  axis  is  kept  pointing  always  the  same  way  while 
the  globe  swims  around,  things  will  correspond  to  the  motion  of  the 
earth  around  the  sun. 

124.  Effects  on  Temperature. — The  changes  in  the  dura- 
tion of  insolation  (exposure  to  sunshine)  at  any  place  involve 
changes  of  temperature,  thus  producing  the  seasons.  It  is 
clear  that  the  surface  of  the  soil  at  any  place  in  the  northern 
hemisphere  will  receive  daily  from  the  sun  more  than  the. 
average  amount  of  heat  when- 
ever he  is  north  of  the  celestial 
equator,  and  for  two  reasons :  — 

1.  Sunshine  lasts  more  than 
half  the  day. 

2.  The  mean  altitude  of  the 
sun  during  the  day  is  greater 

than  the  average,  since   he   is  FIG  16 

higher  at  noon  than  at  the  time      Effect  of  Sun's  Elevation  on  Amount  of 

of  the  equinox,  and  in  any  case  Heat  imParte<*  to  ^  sou. 

reaches  the  horizon  at  rising  and  setting. 

Now  the  more  obliquely  the  rays  strike,  the  less  heat  they 
bring  to  each  square  inch  of  surface,  as  is  obvious  from  Fig. 
16.  A  beam  of  sunshine  which  would  cover  the  surface  AC, 
if  received  squarely,  will  be  spread  over  a  much  larger  sur- 
face, Ac,  if  it  falls  at  the  angle  h.  The  difference  in  favor  of 
vertical  rays  is  further  exaggerated  by  the  absorption  of  heat 
in  our  atmosphere,  because  the  rays  that  are  nearly  horizontal 
have  to  traverse  a  much  greater  thickness  of  air  before  reach- 
ing the  ground. 

For  these   two   reasons,   therefore,   the   temperature   rises 


86  PRECESSION   OF  THE   EQUINOXES.  [§  124 

rapidly  for  a  place  in  the  northern  hemisphere  as  the  sun 
comes  north  of  the  equator.  We,  of  course,  recei\e  the  most 
heat  in  twenty-four  hours  at  the  time  of  the  summer  solstice ; 
but  this  is  not  the  hottest  time  of  the  summer.  The  weather 
is  then  getting  hotter,  and  the  maximum  will  not  be  reached 
until  the  increase  ceases ;  i.e.,  not  until  the  amount  of  heat 
lost  in  twenty-four  hours  equals  that  received  in  the  same 
time.  This  maximum  is  reached  in  our  latitude  about  the  1st 
of  August.  For  similar  reasons  the  minimum  temperature  in 
winter  occurs  about  Feb.  1st. 

125.  Precession  of  the  Equinoxes.  —  This  is  a  slow  westward 
motion  of  the  equinoxes  along  the  ecliptic.     In  explaining  the 
seasons  we  have  said  (Art.  123)  that  the  earth  keeps  its  axis 
nearly  parallel  to  itself  during  its  annual  revolution.     It  does 
not  maintain   strict   parallelism,  however,  but  owing  to  the 
attraction  of  the  sun  and  moon  on  that  portion  of  the  mass  of 
the  earth  which  projects,  like  an  equatorial  ring,  beyond  the 
true  spherical  surface,  the  earth's  axis  continually  but  slowly 
shifts  its  place,  keeping  always  nearly  the  same  inclination  to 
the  plane  of  the  ecliptic,  so  that  its  pole  revolves  in  a  small 
circle  of  23^-°  radius  around  the  pole  of  the  ecliptic  once  in 
25,800  years.     Of  course  the  celestial  equator  must  move  also, 
since  it  has  to  keep  everywhere  just  90°  from  the  celestial 
pole ;  and,  as  a  consequence,  the  equinoxes  move  westward  on 
the  ecliptic  about   50".2   each  year,  as  if  to  meet  the  sun. 
This  motion  of  the  equinox  was  called  '  precession '  by  Hip- 
parchus,  who   discovered1  it   about   125  B.C.,  but  could  not 
explain  it.     The  explanation  was  not  reached  until  the  time  of 
Newton,  about  200  years  ago. 

126.  Effect  of  Precession  upon  the  Pole  and  the  Zodiac.  — 

At  present  the  Pole-star,  Alpha  Ursae  Minoris,  is  about  1^° 

1  He  discovered  it  by  finding  that  in  his  time  the  place  of  the  equinox 
among  the  stars  was  no  longer  the  same  that  it  used  to  be  in  the  days  of 
Homer  and  Hesiod,  several  hundred  years  before. 


§  126]  THE  YEAR   AND  THE   CALENDAR.  87 

from  the  pole,  while  in  the  time  of  Hipparchus  the  distance 
was  fully  12°.  During  the  next  century  the  distance  will 
diminish  to  about  30',  and  then  begin  to  increase. 

If  upon  the  celestial  globe  we  trace  a  circle  of  23^-°  radius, 
around  the  pole  of  the  ecliptic  as  a  centre,  it  will  mark  the 
track  of  the  celestial  pole  among  the  stars. 

It  passes  not  very  far  from  Alpha  Lyrse  (Vega),  on  the  opposite 
side  of  the  circle  from  the  present  Pole-star ;  about  12,000  years  hence 
Vega  will,  therefore,  be  the  Pole-star.  Reckoning  backwards,  we  find 
that  some  4000  years  ago  Alpha  Draconis  (Thuban)  was  the  Pole-star, 
and  about  3£°  from  the  pole. 

Another  effect  of  precession  is  that  the  signs  of  the  zodiac 
do  not  now  agree  with  the  constellations  which  bear  the  same 
name.  The  sign  of  Ares  is  now  in  the  constellation  of  Pisces, 
and  so  on ;  each  sign  having  "  backed "  bodily,  so  to  speak, 
into  the  constellation  west  of  it. 

The  forces  which  cause  precession  do  not  act  quite  uni- 
formly, and  as  a  result  the  rapidity  of  the  precession  varies 
somewhat,  and  there  is  also  a  slight  tipping  or  nodding  of  the 
earth's  axis  which  is  called  nutation.  (For  a  fuller  account  of 
the  whole  matter,  see  General  Astronomy,  Arts.  209-215.) 


THE  YEAE  AND  THE  CALENDAR 

127.  Three  different  kinds  of  "year"  are  now  recognized, 
—  the  Sidereal,  the  Tropical  (or  Equinoctial))  and  the  Anom- 
alistic. 

The  sidereal  year,  as  its  name  implies,  is  the  time  occu- 
pied by  the  sun  in  apparently  completing  the  circuit  from  a 
given  star  to  the  same  star  again.  Its  length  is  365  days, 
6  hours,  9  minutes,  9  seconds.  From  the  mechanical  point  of 
view,  this  is  the  true  year ;  i.e.,  it  is  the  time  occupied  by  the 
earth  in  completing  its  revolution  around  the  sun  from  a  given 
direction  in  space  to  the  same  direction  again. 


88  THE  CALENDAR.  [§  127 

The  tropical  year  is  the  time  included  between  two  successive 
passages  of  the  vernal  equinox  by  the  sun.  Since  the  equinox 
moves  yearly  50".2  towards  the  west,  the  tropical  year  is 
shorter  than  the  sidereal  by  about  20  minutes,  its  length  being 
365  days,  5  hours,  48  minutes,  36  seconds.  Since  the  seasons 
depend  on  the  sun's  place  with  respect  to  the  equinox,  the  tropical 
year  is  the  year  of  chronology  and  civil  reckoning. 

The  third  kind  of  year  is  the  anomalistic  year,  —  the  time  between 
two  successive  passages  of  the  perihelion  by  the  earth.  Since  the  line 
of  apsides  of  the  earth's  orbit  makes  an  eastward  revolution  once  in 
about  108,000  years,  this  kind  of  year  is  nearly  5  minutes  longer  than 
the  sidereal,  its  length  being  365  days,  6  hours,  13  minutes,  48  sec- 
onds. It  is  but  little  used  except  in  calculations  relating  to  perturba- 
tions of  the  planets. 

128.  The  Calendar.  —  The  natural  units  of  time  are  the 
day,  the  month  and  the  year.  The  day  is  too  short  for  con- 
venience in  dealing  with  considerable  periods,  such  as  the  life 
of  a  man,  for  instance ;  and  the  same  is  true  even  of  the 
month ;  so  that  for  all  chronological  purposes  the  tropical  year 
(the  year  of  the  seasons)  has  always  been  employed.  At  the 
same  time,  so  many  religious  ideas  and  observations  have  been 
connected  with  the  changes  of  the  moon,  that  there  has  been  a 
constant  struggle  to  reconcile  the  month  with  the  year.  Since 
the  two  are  incommensurable,  no  really  satisfactory  solution  is 
possible,  and  the  modern  calendar  of  civilized  nations  entirely 
disregards  the  lunar  phases.  In  early  times  the  calendar  was 
in  the  hands  of  the  priesthood,  and  was  mainly  lunar,  the 
seasons  being  either  disregarded,  or  kept  roughly  in  place 
by  the  occasional  putting  in  or  dropping  of  a  month.  The 
Mohammedans  still  use  a  purely  lunar  calendar,  having  a 
"  year  "  of  twelve  months,  which  contains  alternately  354  and 
355  days.  In  their  reckoning  the  seasons  fall  continually  in 
different  months,  and  their  calendar  gains  on  ours  about  one 
year  in  thirty-three. 


§  129]  THE  JULIAN  CALENDAR.  89 

129.  The  Julian  Calendar.  —  When  Julius  Caesar  came  into 
power,   he  found  the  Roman  calendar  in  a  state  of  hopeless 
confusion.     He,  therefore,  with  the  advice  of  Sosigenes,  the 
astronomer,  established  (B.C.  45)  what  is  known  as  the  Julian 
Calendar,  which  still,  either  untouched  or  with  a  trifling  mod- 
ification, continues  in  use  among  civilized  nations.     Sosigenes 
discarded  all  reference   to  the  moon's  phases,  and  adopting 
365J  days  as  the  true  length  of  the  year,  he  ordained  that 
every  fourth  year  should  contain  366  days,  —  the  extra  day 
being  inserted  by  repeating  the  sixth  day  before  the  Calends 
of  March  (whence  such  a  year  is  called  "  Bissextile ").     He 
also   transferred  the   beginning   of    the  year,   which  before 
Caesar's  time  had  been  in  March  (as  is  indicated  by  the  names 
of  several  of  the  months,  —  December,  the  tenth  month,  for 
instance),  to  Jan.  1st. 

Caesar  also  took  possession  of  the  month  Quintilis,  naming  it  July 
after  himself.  His  successor,  Augustus,  in  a  similar  manner  appropri- 
ated the  next  month,  Sextilis,  calling  it  August,  and  to  vindicate  his 
dignity  and  make  his  month  as  long  as  his  predecessor's  he  added  to 
it  a  day  stolen  from  February. 

The  Julian  calendar  is  still  used  unmodified  in  the  Greek 
Church,  and  also  in  many  astronomical  reckonings. 

130.  The  Gregorian  Calendar.  —  The  true  length  of    the 
tropical  year  is  not  365^  days,  but  365  days,  5  hours,  48  min- 
utes, 46  seconds,  leaving  a  difference  of  11  minutes  and  14 
seconds  by  which  the  Julian  year  is  too  long.     This  difference 
amounts  to  a  little  more  than  three  days  in  400  years.     As  a 
consequence  the  date  of  the  vernal  equinox  comes  continually 
earlier  and  earlier  in  the  Julian  calendar,  and  in  1582  it  had 
fallen  back  to  the  llth  of  March  instead  of  occurring  on  the 
21st,  as  it  did  at  the  time  of  the  Council  of  Nice  (A.D.  325). 
Pope   Gregory,  therefore,  under  the   astronomical   advice   of 
Clavius,  ordered  that  the  calendar  should  be  restored  by  add- 
ing ten  days,  so  that  the  day  following  Oct.  4th,  1582,  should 


90  THE  GEEGOBIAN   CALENDAR.  [§  130 

be  called  the  15th.  instead  of  the  5th ;  further,  to  prevent  any 
future  displacement  of  the  equinox,  he  decreed  that  thereafter 
only  such  century  years  should  be  leap  years  as  are  divisible 
by  400.  Thus  1700,  1800,  1900,  and  2100  are  not  leap 
years,  but  1600  and  2000  are.  The  change  was  immediately 
adopted  by  all  Catholic  countries,  but  the  Greek  Church  and 
most  Protestant  nations  refused  to  recognize  the  Pope's  au- 
thority. The  new  calendar  was,  however,  at  last  adopted  in 
England  in  1752.  At  present  (since  the  year  1800  was  a  leap 
year  in  the  Julian  calendar  and  not  in  the  Gregorian)  the  dif- 
ference between  the  two  calendars  is  twelve  days ;  but  it  will 
become  thirteen  in  1900,  which  will  not  be  a  leap  year  with 
us,  though  it  will  in  Eussia. 


131]  THE  MOON.  91 


CHAPTER  V. 

THE  MOON.  —  HER  ORBITAL  MOTION  AND  THE  MONTH.  — 
DISTANCE,  DIMENSIONS,  MASS,  DENSITY,  AND  FORCE  OF 
GRAVITY. — ROTATION  AND  ITERATIONS. — PHASES. — 
LIGHT  AND  HEAT.  —  PHYSICAL  CONDITION.  —  TELE- 
SCOPIC ASPECT  AND  PECULIARITIES  OF  THE  LUNAR 
SURFACE. 

131.  NEXT  to  the  sun,  the  moon  is  the  most  conspicuous, 
and  to  us  the  most  important,  of  the  heavenly  bodies  ;  in  fact, 
she  is  the  only  one  except  the  sun,  which  exerts  the  slightest 
perceptible  influence  upon  the  interests  of  human  life.     She 
owes  her  conspicuousness  and  her  importance,  however,  solely 
to  her  nearness  ;  for  she  is  really  a  very  insignificant  body  as 
compared  with  stars  and  planets. 

132.  The  Moon's  Apparent  Motion ;  Definition  of  Terms,  etc. 

—  One  of  the  earliest  observed  of  astronomical  phenomena 
must  have  been  the  eastward  motion  of  the  moon  with  refer- 
ence to  the  sun  and  stars,  and  the  accompanying  change  of 
phase.  If,  for  instance,  we  note  the  moon  to-night  as  very 
near  some  conspicuous  star,  we  shall  find  her  to-morrow  night 
at  a  point  considerably  farther  east,  and  the  next  night 
farther  yet ;  she  changes  her  place  about  13°  daily,  and  makes 
the  complete  circuit  of  the  heavens,  from  star  to  star  again,  in 
about  27J  days.  In  other  words,  she  revolves  around  the 
earth  in  that  time,  while  she  accompanies  us  in  our  annual 
journey  around  the  sun.  Since  the  moon  moves  eastward 
among  the  stars  so  much  faster  than  the  sun  (which  takes  a 
year  in  going  once  around),  she  overtakes  and  passes  him  at 


92  SIDEREAL  AND   SYNODIC   MONTHS.  C§  ^ 

regular  intervals  ;  and  as  her  phases  depend  upon  her  apparent 
position  with  reference  to  the  sun,  this  interval  from  new 
moon  to  new  moon  is  specially  noticeable,  and  is  what  we 
ordinarily  understand  as  the  "  month." 

The  angular  distance  of  the  moon  east  or  west  of  the  sun  at 
any  time  is  called  her  Elongation.  At  new  moon  it  is  zero, 
and  the  moon  is  said  to  be  in  Conjunction.  At  full  moon  the 
elongation  is  180°,  and  she  is  said  to  be  in  Opposition.  In 
either  case  the  moon  is  in  Syzygy.  (Syzygy  means  "yoked 
together,"  the  sun,  moon,  and  earth  being  then  nearly  in  line.) 
When  the  elongation  is  90°,  she  is  said  to  be  in  Quadrature. 

133.  Sidereal  and  Synodic  Months.  —  The  sidereal  month  is 
the  time  it  takes  the  moon  to  make  her  revolution  from  a  given 
star  to  the  same  star  again ;  its  length  is  27^  days  (27  days,  7 
hours,  43  minutes,  11.545  seconds).  The  mean  daily  motion, 
therefore,  is  360°  divided  by  this,  or  13°  11'  (nearly).  The 
sidereal  month  is  the  true  month  from  the  mechanical  point 
of  view. 

The  synodic  month  is  the  time  between  two  successive  con- 
junctions or  oppositions;  i.e.,  between  two  successive  new  or 
full  moons.  It.;  average  length  is  about  29^-  days  (29  days, 
12  hours,  44  minutes,  2.864  seconds),  but  it  varies  consider- 
ably on  account  of  the  eccentricity  of  the  moon's  orbit. 

If  M  be  the  length  of  the  moon's  sidereal  period  in  days,  E  the 
length  of  the  sidereal  year,  and  S  that  of  the  synodic  month,  the  three 

quantities  are  connected  by  a  simple  relation  easily  demonstrated.    — 

M 
is  the  fraction  of  a  circumference  moved  over  by  the  moon  in  a  day. 

Similarly,  —  is  the  apparent  daily  motion  of  the  sun.     The  difference 

E 

is  the  amount  which  the  moon  gains  on  the  sun  daily.  Now  it  gains 
a  whole  revolution  in  one  synodic  month  of  S  days,  and  therefore 

must  gain  daily  —  of  a  circumference.    Hence  we  have  the  important 

S 

equation  _1  __L_J: 

M     E     S 


§  133]  MOON'S   PATH  AMONG  THE   STABS.  93 

which  is  known  as  the  equation  of  synodic  motion.  In  a  sidereal  year 
the  number  of  sidereal  months  is  exactly  one  greater  than  the  num- 
ber of  synodic  months,  the  numbers  being  respectively  13.369  +  and 
12.369  +. 

134.  The  Moon's  Path  among  the  Stars.  —  By  observing  the 
moon's   right  ascension  and  declination  daily  with  suitable 
instruments,  we  can  map  out  its  apparent  path,  just  as  in  the 
case  of  the  sun  (Art.  116) .    This  path  turns  out  to  be  (very 
nearly)  a  great  circle,  inclined  to  the  ecliptic  at  an  angle  of 
5°  8'.     The  two  points  where  it  cuts  the  ecliptic  are  called  the 
"nodes,"  the  ascending  node  being  where  the  moon  passes 
from  the  south  side  to  the  north  side  of  the  ecliptic,  while  the 
opposite  node  is  called  the  descending  node. 

The  moon  at  the  end  of  the  month  never  comes  back  exactly  to  the 
point  of  beginning  among  the  stars,  on  account  of  the  so-called  "  per- 
turbations" of  her  orbit,  due  mostly  to  the  attraction  of  the  sun. 
One  of  the  most  important  of  these  perturbations  is  the  "  regression 
of  the  nodes."  These  slide  westward  on  the  ecliptic  just  as  the  vernal 
equinox  does  (precession),  but  much  faster,  completing  their  circuit 
in  about  19  years  instead  of  26,000. 

135.  Interval  between  the  Moon's  Successive  Transits ;  Daily 
Retardation.  —  Owing  to  the  eastward  motion  of  the  moon  it 
comes  to  the  meridian  about  51  minutes  later  each  day,  on 
the  average ;   but  the  retardation  ranges  all  the  way  from  38 
minutes  to  66  minutes,  on  account  of  the  variation  in  the  rate 
of  the  moon's  motion. 

The  average  retardation  of  the  moon's  rising  and  setting  is 
also,  of  course,  the  same  51  minutes ;  but  the  actual  retarda- 
tion is  still  more  variable  than  that  of  the  meridian  transits, 
depending  to  some  extent  on  the  latitude  of  the  observer  as 
well  as  on  the  variations  in  the  moon's  motion.  At  New 
York  the  range  is  from  23  minutes  to  1  hour  and  17  minutes ; 
that  is  to  say,  on  some  nights  the  rising  of  the  moon  is  only 
23  minutes  later  than  on  the  preceding  night,  while  at  other 


94  HARVEST  AND  HUNTER'S   MOON.  [§  135 

times  it  is  more  than  an  hour  and  a  quarter  behindhand.  In 
high  latitudes  the  differences  are  still  greater.  In  very  high 
latitudes  the  moon,  when  it  has  its  greatest  possible  declina- 
tion, becomes  circumpolar  for  a  certain  time  each  month, 
and  remains  visible  without  setting  at  all  (like  the  midnight 
sun)  for  a  greater  or  less  number  of  days,  according  to  the 
latitude  of  the  observer. 

136.  Harvest  and  Hunter's   Moon.  — The  full  moon  that 
occurs  nearest  the  autumnal  equinox  is  called  the  '  harvest 
moon ' ;  the  one  next  following,  the  '  hunter's  moon.'     At  that 
time  of  the  year  the  moon,  while  nearly  full,  rises  for  several 
consecutive  nights  almost  at  the  same  hour,  so  that  the  moon- 
light evenings  last  for  an  unusually  long  time.     The  phenome- 
non, however,  is  much  more  striking  in  Northern  Europe  and 
in  Canada  than  in  the  United  States. 

137.  Form  of  the  Moon's   Orbit.  —  By  observation  of  the 
moon's  apparent  diameter  in  connection  with  observations  of 
her  place  in  the  sky,  we  can  determine  the  form  of  her  orbit 
around  the  earth  in  the  same  way  that  the  form  of  the  earth's 
orbit  around  the  sun  was  worked  out  (see  Appendix,  Art. 
428).     The   moon's   apparent  diameter  ranges  from  33'  33", 
when  as  near  the   earth  as  possible,  to  29'  24",  when  most 
remote ;  and  her  orbit  turns  out  to  be  an  ellipse  like  that  of 
the  earth  around  the  sun,  but  of  much  greater  eccentricity, 
averaging  about  ^  (as  against  -g^).     We  say  "  averaging  "  be- 
cause the  actual  eccentricity  is  variable,  on  account  of  pertur- 
bations. 

The  point  of  the  moon's  orbit  nearest  the  earth  is  called  the 
Perigee,  that  most  remote  the  Apogee,  and  the  indefinite  line 
passing  through  these  points  the  Line  of  Apsides,  while  the 
major  axis  is  that  portion  of  this  line  which  lies  between  the 
perigee  and  apogee.  This  line  of  apsides  is  in  continual 
motion,  on  account  of  perturbations  (just  as  the  line  of  nodes 


§  137]  THE  MOON^S  DISTANCE.  05 

is,  Art.  134),  but  it  moves  eastward  instead  of  westward,  com- 
pleting its  revolution  in  about  nine  years.  In  her  revolution 
about  the  earth,  the  moon  observes  the  same  law  of  equal 
areas  that  the  earth  does  in  her  orbit  around  the  sun  (Art. 
121). 

THE  MOON'S  DISTANCE. 

138.  In  the  case  of  any  heavenly  body,  one  of  the  first  and 
most   fundamental  inquiries  relates  to  its  distance  from  us : 
until  the  distance  has  been  somehow  measured  we  can  get  no 
knowledge  of  the  real  dimensions  of  its  orbit,  nor  of  the  size, 
mass,  etc.,  of  the  body  itself.    The  problem  is  usually  solved 
by  measuring  the  apparent  "  parallactic  "  displacement  of  the 
body,   as   seen   by   observers    at  widely   separated    stations. 
Before   proceeding  farther,   we  must,   therefore,   say  a  few 
words  upon  the  subject  of  parallax. 

139.  Parallax. — In   general  the  word  "parallax"  means 
the  difference  between  the  directions  of  a  heavenly  body  as 
seen  by  the  observer,  and  as  seen  from  some  standard  point 
of  reference.     The  annual  or  heliocentric  parallax  of  a  star  is 
the  difference  of  the  star's  direction  as  seen  from  the  earth 
and  from  the  sun.     The  diurnal  or  geocentric  parallax  of  the 
sun,  the  moon,  or  a  planet,  is  the  difference  between  its  direc- 
tion as  seen  from  the  centre  of  the  earth  and  from  the  obser- 
ver's station  on  the  earth's  surface ;  or,  what  comes  to  the  same 
thing,  the  geocentric  parallax  is  the  angle  at  the  body  made  by 
two  lines  drawn  from  it,  one  to  the  observer,  the  other  to  the  centre 
of  the  earth.     (Stars  have  no  geocentric  parallax  j  the  earth  as 
seen  from  them  is  a  mere  point.) 

In  Fig.  17,  the  parallax  of  the  body  P  is  the  angle  OPC. 
Obviously  this  diurnal  parallax  is  zero  for  a  body  directly  over- 
head at  Z,  and  is  the  greatest  possible  for  a  body  on  the  hori- 
zon, as  at  Ph. 


96 


PARALLAX   AND  DISTANCE. 


[§139 


Moreover,  and  this  is  to  be  specially  noted,  this  parallax  of 
a  body  at  the  horizon  —  the  "  horizontal  parallax  "  —  is  simply 
the  wngular  semi-diameter  of  the  earth  as  seen  from  the  body. 
When,  for  instance,  we  say  that  the  moon's  horizontal  parallax 
is  57',  it  is  equivalent  to  saying  that  seen  from  the  moon  the 
earth  appears  to  have  a  diameter  of  114'.  In  the  same  way, 
since  the  sun's  parallax  is  8".8,  the  diameter  of  the  earth  as 
seen  from  the  sun  is  17".6. 


140.  Relation  between  Parallax  and  Distance. — When  the 
horizontal  parallax  of  any  heavenly  body  is  ascertained,  its  dis- 
tance follows  at  once  through 
our  knowledge  of  the  earth's 
dimensions.  If  we  know  how 
large  a  ball  of  given  size 
appears,  we  can  tell  how  far 
away  it  is ;  if  we  know  how 
large  the  earth  looks  from  the 
moon,  we  can  find  the  distance 
between  them.  Thus,  when  in 
the  triangle  CPhO,  Fig.  17,  we 
know  the  angle  at  P^  and  the 
side  CO,  the  radius  of  the 
earth,  we  can  compute  CPh  by 
a  very  easy  trigonometrical 

calculation.     Evidently  the  more  remote  the  body,  the  smaller 
its  parallax. 

Since  the  radius  of  the  earth  varies  slightly  in  different  lati- 
tudes, we  take  the  equatorial  radius  as  a  standard,  and  the 
equatorial  horizontal  parallax  is  the  earth's  equatorial  semi- 
diameter  as  seen  from  the  body.  It  is  this  which  is  usually 
meant  when  we  speak  simply  of  "  the  parallax  "  of  the  moon, 
of  the  sun,  or  of  a  planet  without  adding  any  qualification 
(but  never  when  we  speak  of  the  parallax  of  a  star ;  then  we 
always  mean  the  annual  parallax). 


FIG.  17. —  Diurnal  Parallax. 


§  141]  DIAMETER,   ETC.,   OF  THE  MOON.  97 

141.  Parallax,  Distance,  and  Velocity  of  the  Moon. — The 

moon's  equatorial  horizontal  parallax  found  by  corresponding 
observations  made  at  different  parts  of  the  earth,  is  3422"  (57' 
2")  according  to  Neison,  but  varies  considerably  on  account  of 
the  eccentricity  of  the  orbit.  From  this  parallax  we  find 
that  the  moon's  average  distance  from  the  earth  is  about  60.3 
times  the  earth's  equatorial  radius,  or  238,840  miles,  with  an 
uncertainty  of  perhaps  20  miles. 

The  maximum  and  minimum  values  of  the  moon's  distance  are 
given  by  Neison  as  252,972  and  221,617  miles.  It  will  be  noted  that 
the  average  distance  is  not  the  mean  of  the  two  extremes. 

Knowing  the  size  and  form  of  the  moon's  orbit,  the  velocity 
of  her  motion  is  easily  computed.  It  averages  a  little  less 
than  2300  miles  an  hour,  or  about  3350  feet  per  second.  Her 
mean  apparent  angular  velocity  among  the  stars  is  about  33', 
which  is  just  a  little  greater  than  the  apparent  diameter  of 
the  moon  itself. 

142.  Diameter,  Area,  and  Bulk  of  the  Moon.  —  The  mean 
apparent  diameter  of  the  moon  is  31'  7".     Knowing  its  dis- 
tance, its  real  diameter  comes  out  2163  miles.     This  is  0.273 
of  the  earth's  diameter. 

Since  the  surfaces  of  globes  vary  as  the  squares  of  their 
diameters,  and  their  volumes  as  the  cubes,  this  makes  the  sur- 
face area  of  the  moon  equal  to  about  JT  of  the  earth's,  and  the 
volume  (or  bulk)  almost  exactly  -fa  of  the  earth's. 

No  other  satellite  is  nearly  as  large  as  the  moon  in  comparison  with 
its  primary  planet.  The  earth  and  moon  together,  as  seen  from  a  dis- 
tance, are  really  in  many  respects  more  like  a  double  planet  than  like 
a  planet  and  satellite  of  ordinary  proportions.  At  a  time,  for  instance, 
when  Venus  happens  to  be  nearest  the  earth  (at  a  distance  of  about 
twenty-five  millions  of  miles),  her  inhabitants  (if  she  has  any)  would 
see  the  earth  just  about  as  brilliant  as  Venus  herself  at  her  best 
appears  to  us,  and  the  moon  would  be  about  as  bright  as  Sirius,  oscil- 


98  MASS,  DENSITY,   ETC.,   OF  THE  MOON.  [§  143 

lating  backwards  and  forwards  about  half  a  degree  each  side  of  the 
earth,  once  a  month. 

143.  Mass,  Density,  and  Superficial  Gravity  of  the  Moon. 

—  Her  mass  is  about  ^5-  of  the  earth's  mass  (0.0125).  The 
actual  measurement  of  the  moon's  mass  is  an  extremely  diffi- 
cult problem,  and  the  methods  pursued  are  quite  beyond  the 

scope  of  this  book.     Since  the  density  is  equal  to  TT  iass  ,  the 

Volume 

density  of  the  moon  as  compared  to  that  of  the  earth  is  found 
to  be  0.613,  or  about  3.4  the  density  of  water  (the  earth's 
density  being  5.58).  This  is  a  little  above  the  average  den- 
sity of  the  rocks  which  compose  the  crust  of  the  earth. 

The  '  superficial  gravity,'  or  the  attraction  of  the  moon  for 
bodies  at  its  surface,  is  about  one-sixth  that  at  the  surface  of 
the  earth.  This  is  a  fact  that  must  be  borne  in  mind  in  con- 
nection with  the  enormous  scale  of  the  craters  on  the  moon. 
Volcanic  forces  there  would  throw  materials  to  a  vastly  greater 
distance  than  on  the  earth. 

144.  Rotation  of  the  Moon. — The  moon  turns  on  its  axis 
once  a  month,  in  exactly  the  time  occupied  by  its  revolution 
around  the  earth :  its  day  and  night  are,  therefore,  each  nearly 
a  fortnight  in  length,  and  in  the  long  run  it  keeps  the  same 

Oside  always  toward  the  earth.  We  see  to- 
day precisely  the  same  face  of  the  moon 
' '^\  which  Galileo  did  when  he  first  looked  at  it 
with  his  telescope.  The  opposite  face  has 
never  been  seen  from  the  earth,  and  prob- 
ably never  will  be. 


tf 


It  is  difficult  for  some  to  see  why  a  motion  of 
this  sort  should  be  considered  a  rotation  of  the 
moon,  since  it  is  essentially  like  the  motion  of  a 


FIG.  18.  ball  carried  on  a  revolving  crank  (Fig.  18).   Such 

a  ball,  they  say,  "  revolves  around  the  shaft,  but  does  not  rotate  on 
its  own  axis."    It  does  rotate,  however  j  for  if  we  mark  one  side  of 


§  144]  THE  MOON'S   PHASES.  99 

the  ball,  we  shall  find  the  marked  side  presented  successively  to  every 
point  of  the  compass  as  the  crank  turns  around,  so  that  the  ball  turns 
on  its  own  axis  as  really  as  if  it  were  whirling  upon  a  pin  fastened  to 
the  table.  By  virtue  of  its  connection  with  the  crank,  the  ball  has 
two  distinct  motions, —  (1)  the  motion  of  translation,  which  carries  its 
centre  in  a  circle  around  the  shaft ;  (2)  an  additional  motion  of  rota- 
tion around  a  line  drawn  through  its  centre  of  gravity  parallel  to  the 
shaft. 

Rotation  consists  essentially  in  this  :  A  line  connecting  any  two  points 
in  the  rotating  body,  and  produced  to  the  celestial  sphere,  will  sweep  out  a 
circle  upon  it.  In  every  rotating  body,  one  line  can  be  drawn  through 
the  centre  of  the  body,  however,  so  that  the  circle  described  by  it  in 
the  sky  will  be  infinitely  small.  This  is  the  axis  of  the  body. 

145.  Librations.  —  While  in  the  long  run  the  moon  keeps  the 
same  face  towards  the  earth,  it  is  not  so  from  day  to  day.    With  refer- 
ence to  the  centre  of  the  earth,  it  is  continually  oscillating  a  little, 
and  these  oscillations  constitute  what  are  called  "Librations,"  of 
which  we  distinguish  three;  viz.,  (1)  the  libration  in  latitude,  by 
which  the  north  and  south  poles  are  alternately  presented  to  the  earth  ; 
(2)  the  libration  in  longitude,  by  which  the  east  and  west  sides  of  the 
moon  are  alternately  tipped  a  little  towards  us ;  and  (3)  the  diurnal 
libration,  which  enables  us  to  look  over  whatever  edge  of  the  moon  is 
uppermost  when  it  is  near  the  horizon.     Owing  to  these  librations  we 
see  considerably  more  than  half  of  the  moon's  surface  at  one  time 
and  another.     About  41  per  cent  of  it  is  always  visible ;  41  per  cent 
never  visible,  and  a  belt  at  the  edge  of  the  moon,  covering  about  18 
per  cent  is  rendered  alternately  visible  and  invisible  by  libration. 

146.  Phases  of  the  Moon.  —  Since  the  moon  is  an  opaque 
globe  shining  merely  by  reflected  light,  we  can  only  see  that 
hemisphere  of  her  surface  on  which  the  sun  is  shining,  and  of 
the.  illuminated  hemisphere  only  that  portion  which  happens 
to  be  turned  towards  the  earth. 

When  the  moon  is  between  the  earth  and  the  sun  (new 
moon),  the  side  presented  to  us  is  dark,  and  the  moon,  is 
then  invisible.  A  week  later,  at  the  end  of  the  first  quarter, 
half  of  the  illuminated  hemisphere  is  visible,  and  we  have  the 


100 


THE  MOON'S   PHASES. 


[§U6 


half-moon  just  as  we  do  a  week  after  the  full.  Between  the 
new  moon  and  the  half-moon,  during  the  first  and  last  quarters 
of  the  lunation,  we  see  less  than  half  of  the  illuminated  por- 
tion, and  then  have  the  "crescent"  phase.  Between  half- 
moon  and  the  full  moon,  during  the  second  and  third  quarters 


FIG.  19.  —  The  Moon's  Phases. 

of  the  lunation,  we  see  more  than  half  of  the  moon's  illumi- 
nated side,  and  we  have  then  what  is  called  the  "  gibbous  " 
phase. 

Fig.  19  (in  which  the  light  is  supposed  to  come  from  a  point  far 
above  the  circle  which  represents  the  moon's  orbit)  shows  the  way  in 
which  the  phases  are  distributed  through  the  month. 


§  146]  EARTH-SHINE   ON   THE  MOON.  101 

The  line  which  separates  the  dark  portion  of  the  disc  from 
the  bright  is  called  the  Terminator,  and  is  always  a  semi- 
ellipse,  since  it  is  a  semicircle  viewed  obliquely,  as  shown  by 
Fig.  20,  A.  Draughtsmen  sometimes  incorrectly  represent  the 
crescent  form  by  a  construction  like  Fig.  20,  J5,  in  which  a 
smaller  circle  has  a  portion  cut  out  of  it  by  an  arc  of  a  larger 
one.  It  is  to  be  noticed  also  that  a&, 
the  line  which  joins  the  "  cusps "  or 
points  of  the  crescent,  is  always  perpen- d<(  J[  \n]f 
dicular  to  a  line  drawn  from  the  moon 
to  the  sun,  so  that  the  horns  are  always 
turned  directly  away  from  the  sun.  The 
precise  position  in  which  they  will  stand 
at  any  time  is,  therefore,  perfectly  predictable,  and  has  nothing 
whatever  to  do  with  the  weather.  (Pupils  have  probably 
heard  of  the  "  wet  moon  "  and  "  dry  moon  "  superstition.) 

147.  Earth-shine  on  the  Moon.  —  Near  the  time  of  new 
moon,  the  portion  of  the  moon's  disc  which  does  not  get  the 
sunlight  is  easily  visible,  illuminated  by  a  pale  reddish  light. 
This  light  is  earth-shine,  —  the  earth  as  seen  from  the  moon 
being  then  nearly  full.  The  red  color  is  due  to  the  fact  that 
the  light  sent  to  the  moon  from  the  earth  has  passed  twice 
through  our  atmosphere,  and  so  has  acquired  the  sunset  tinge. 
Seen  from  the  moon,  the  earth  would  be  itself  a  magnificent 
moon  about  2°  in  diameter,  showing  the  same  phases  as  the 
moon  does  itself. 

Taking  everything  into  account,  the  earth-shine  is  probably  fifteen 
to  twenty  times  as  strong  as  the  light  of  the  moon  at  similar  phases. 
Since  the  moon  keeps  always  the  same  face  towards  the  earth,  the 
earth  is  visible  only  from  that  part  of  the  moon  which  faces  us,  and 
remains  nearly  stationary  in  the  lunar  sky,  neither  rising  nor  setting. 
It  is  easy  to  see  that  she  would  be  a  very  beautiful  object,  on  account 
of  the  changes  which  would  be  continually  going  on  upon  her  surface 
due  to  snow-storms,  clouds,  growth  of  vegetation,  etc. 


102  ABSENCE  OF  AIR  AND  WATER.  [§  148 

PHYSICAL  CHARACTERISTICS  OF  THE  MOON. 

148.  Absence  of  Air  and  Water.  —  The  moon's  atmosphere, 
if  there  is  any,  is  extremely  rare,  its  density  at  the  moon's 
surface  being  probably  not  more  than  -3-^  part  of  that  of  our 
own  atmosphere. 

The  evidence  on  the  point  is  twofold :  First,  the  telescopic  appear- 
ance. There  is  no  haze,  shadows  are  perfectly  black ;  there  is  no 
sensible  twilight  at  the  points  of  the  crescent,  and  all  outlines  are  visi- 
ble sharply  and  without  the  least  blurring  such  as  would  be  due  to 
the  intervention  of  an  atmosphere.  Second,  the  absence  of  refraction 
when  the  moon  intervenes  between  us  and  any  distant  body.  When 
the  moon  *  occults '  a  star,  for  instance,  there  is  no  distortion  or  dis- 
coloration of  the  star-disc,  but  both  the  disappearance  and  the  reap- 
pearance are  practically  instantaneous. 

Of  course  if  there  is  no  air,  there  can  be  no  liquid  water, 
since  the  water  would  immediately  evaporate  and  form  an 
atmosphere  of  vapor  if  air  were  not  present.  It  is  not  impos- 
sible, however,  nor  perhaps  improbable,  that  solid  water  (ice 
and  snow)  may  exist  on  the  moon's  surface.  Although  ice  and 
snow  liberate  a  certain  amount  of  vapor,  yet  at  a  low  temper- 
ature the  quantity  would  be  insufficient  to  make  an  atmos- 
phere dense  enough  to  be  observed  from  the  earth. 

If  the  moon  once  formed  a  portion  of  the  earth,  as  is  likely, 
the  absence  of  air  and  water  requires  explanation,  and  there 
have  been  many  interesting  speculations  on  the  subject  into 
which  we  cannot  enter. 

149.  The  Moon's  Light.  —  In  its  quality  moonlight  is  simply 
sunlight,  showing  a  spectrum  identical  in  every  detail  with 
that  of  the  light  coming  from  the  sun  itself,  except  as  the 
intensity  of  different  portions  of  the   spectrum  is   slightly 
altered  by  its  reflection  from  the  lunar  surface. 

The  brightness  of  full  moonlight  as  compared  with  sunlight 
is  about  one  six-hundred-thousandth.  According  to  this,  if  the 


§  1*9]  HEAT   OF   THE   MOON.  103 

whole  visible  hemisphere  were  packed  with  full  moons,  we 
should  receive  from  it  only  about  one-eighth  of  the  light  of  the 
sun. 

The  half-moon  does  not  give  nearly  half  as  much  light  as 
the  full  moon.  Near  the  full  the  brightness  is  suddenly  and 
greatly  increased,  probably  because  at  any  time  except  the 
full  the  moon's  visible  surface  is  more  or  less  darkened  by 
shadows  which  disappear  at  the  moment  of  full. 

The  average  "albedo,"  or  reflecting  power,  of  the  moon's 
surface  is  given  by  Zollner  as  0.174;  i.e.,  the  moon's  surface 
reflects  a  little  more  than  one-sixth  of  the  light  that  falls 
upon  it.  There  are,  however,  great  differences  in  the  bright- 
ness of  the  different  portions  of  the  moon's  surface.  Some 
spots  are  nearly  as  white  as  snow  or  salt,  and  others  as  dark 
as  slate. 

150.  Heat  of  the  Moon.  —  For  a  long  time  it  was  impossible 
to  detect  the  moon's  heat  by  observation.  Even  when  concen- 
trated by  a  large  lens,  it  is  too  feeble  to  be  shown  by  the  most 
delicate  thermometer.  With  modern  apparatus,  however,  it  is 
easy  enough  to  perceive  the  heat  of  lunar  radiation,  though  the 
measurement  is  extremely  difficult.  The  total  amount  of  heat 
sent  by  the  full  moon  to  the  earth  appears  to  be  about  1701007  of 
that  sent  by  the  sun;  i.e.,  the  full  moon  in  two  days  sends 
us  about  as  much  heat  as  the  sun  does  in  one  second. 

A  considerable  portion  of  the  lunar  heat  seems  to  be  simply 
reflected  from  the  surface  like  light,  while  the  rest,  perhaps 
three-fourths  of  the  whole,  is  "obscure  heat";  i.e.,  heat  which 
has  first  been  absorbed  by  the  moon's  surface  and  then  radi- 
ated, like  the  heat  from  a  brick  surface  that  has  been  warmed 
by  the  sunshine. 

As  to  the  temperature  of  the  moon's  surface,  it  is  impossible 
to  be  very  certain.  During  the  long  lunar  night  of  fourteen 
days,  the  temperature  must  inevitably  fall  appallingly  low, 
—  perhaps  200°  or  300°  below  zero.  On  the  other  hand,  the 


104  LUNAR    INFLUENCES.  [§  15° 

lunar  rocks  are  exposed  to  the  sun's  rays  in  a  cloudless  sky 
for  fourteen  days  at  a  time,  so  that  if  they  were  protected  by 
air,  like  the  rocks  upon  the  earth,  they  would  certainly  become 
intensely  heated.  But  there  is  no  air,  and,  on  the  whole,  it  is 
probable  that  the  temperature  never  rises  much  above  the 
freezing-point  of  water,  since  in  the  absence  of  air  the  heat 
would  be  lost  about  as  fast  as  it  is  received,  and  the  condition 
of  things  may  be  supposed  to  be  somewhat  like  that  on  the 
highest  mountains  of  the  earth  (where  there  is  perpetual  snow 
and  ice),  only  more  so. 

151.  Lunar  Influences  on  the  Earth. — The  most  important 
effect  produced  upon  the  earth  by  the  moon  is  the  generation 
of  the  tides  in  co-operation  with  the  sun.     There  are  also  cer- 
tain well-ascertained  disturbances  of  the  terrestrial  magnetism 
connected  with  the  approach  and  recession  of  the  moon  in  its 
oval  orbit;  and  this  ends  the  chapter  of  proved  lunar  influ- 
ences. 

The  multitude  of  current  beliefs  as  to  the  controlling  influ- 
ence of  the  moon's  phases  and  changes  upon  the  weather  and 
the  various  conditions  of  life  are  mostly  unfounded.  It  is 
quite  certain  that  if  the  moon  has  any  influence  at  all  of  the 
sort  imagined,  it  is  extremely  slight ;  so  slight  that  it  has  not 
yet  been  demonstrated,  though  numerous  investigations  have 
been  made  expressly  for  the  purpose  of  detecting  it.  Different 
workers  continually  come  to  contradictory  results. 

152.  The    Moon's    Telescopic   Appearance.  —  Even  to  the 
naked  eye  the  moon  is  a  beautiful  object,  diversified  with  curi- 
ous markings  connected  with  numerous  popular  legends.     In 
a  powerful  telescope  these  naked-eye  markings  vanish,  and 
are  replaced  by  a  multitude  of  smaller  details  which  make  the 
moon,   on  the  whole,  the  most  interesting  of  all  telescopic 
objects  —  especially  to  instruments  of  moderate  size,  say  from 
six  to  ten  inches  in  diameter,  which  generally  give  a  more 


§  152]  THE  MOON'S   SURFACE.  105 

pleasing  view  than  instruments  either  much  larger  or  much 
smaller.  An  instrument  of  this  size,  with  magnifying  powers 
between  250  and  500,  virtually  brings  the  moon  within  a  dis- 
tance ranging  from  1000  to  500  miles.  Any  object  half  a 
mile  in  diameter  on  the  moon  is  distinctly  visible.  A  long 
line  or  streak  even  less  than  a  quarter  of  a  mile  across  can 
easily  be  seen. 

For  most  purposes  the  best  time  to  look  at  the  moon  is  when  it  is 
between  six  and  ten  days  old :  at  the  time  of  full  moon  few  parts  of 
the  surface  are  well  seen.  It  is  evident  that  while  with  the  telescope 
we  should  be  able  to  see  such  objects  as  lakes,  rivers,  forests,  and 
great  cities,  if  they  existed  on  the  moon,  it  would  be  hopeless  to 
expect  to  distinguish  any  of  the  minor  indications  of  life,  such  as 
buildings  or  roads. 

153.  The  Moon's  Surface  Structure. — The  moon's  surface 
for  the  most  part  is  extremely  broken.  The  earth's  mountains 
are  mainly  in  long  ranges,  like  the  Andes  and  Himalayas. 
On  the  moon  the  ranges  are  few  in  number ;  but,  on  the  other 
hand,  the  surface 
is  pitted  all  over 
with  great  craters, 
which  resemble 
very  closely  the 
volcanic  craters  on 
the  earth's  surface, 
though  on  an  im- 
mensely greater 
scale.  The  largest 
terrestrial  craters  FlG<  21> " A  Norraal  Lunar  Crater  (Nasrayth)- 

do  not  exceed  six  or  seven  miles  in  diameter ;  many  of  those 
on  the  moon  are  fifty  or  sixty  miles  across,  and  some  have  a 
diameter  of  more  than  a  hundred  miles,  while  smaller  ones 
from  five  to  twenty  miles  in  diameter  are  counted  by  the 
hundred. 

The  normal  lunar  crater  (Fig.  21)  is  nearly  circular,  sur- 


106  LUNAR   CRATERS   AND   MOUNTAINS.  [§  153 

rounded  by  a  mountain  ring,  which  rises  anywhere  from  1000 
to  20,000  feet  above  the  neighboring  country.  The  floor  within 
the  ring  may  be  either  above  or  below  the  outside  level ;  some 
craters  are  deep,  and  some  are  rilled  nearly  to  the  brim.  Fre- 
quently, in  the  centre  of  the  crater,  there  rises  a  group  of 
peaks  which  attain  the  same  elevation  as  the  encircling  ring, 
and  these  central  peaks  often  show  holes  or  minute  craters 
in  their  summits. 

On   some  portions   of  the  moon  these  craters  stand  very 
thickly.     This  is  especially  the  case  near  the  moon's   south 

pole.  It  is  noticeable, 
also,  that  as  on  the 
earth  the  youngest 
mountains  are  gener- 
ally the  highest,  so  on 
the  moon  the  most  re- 
cent craters  are  gener- 
ally deepest  and  most 
precipitous.  * 

The  height  of  a  lu- 
nar mountain  can  be 
measured  with  consid- 
erable accuracy  by 
means  of  its  shadow. 

The  striking  resem- 
blance of  these  lunar 
craters  to  terrestrial  vol- 
canoes makes  it  natural 
to  assume  that  they  have 

FIG.  22.  —  Gaesendi  (JSTasmyth).  .    .  —,,  . 

a  similar  origin.      This, 

however,  is  not  quite  certain,  for  there  are  considerable  difficulties  in 
the  way  of  the  volcanic  theory,  especially  in  the  case  of  what  are 
called  the  great  "  Bulwark  Plains,"  so  extensive  that  a  person  stand- 
ing in  the  centre  could  not  even  see  the  summit  of  the  surrounding 
ring  at  any  point;  and  yet  there  is  no  line  of  distinction  between 
them  and  the  smaller  craters,  —  the  series  is  continuous.  Moreover, 


§153] 


OTHER   LUNAR   FORMATIONS. 


107 


on  the  earth,  volcanoes  necessarily  require  the  action  of  air  and  water, 
which  do  not  now  exist  on  the  moon ;  so  that  if  these  lunar  craters 
are  really  the  result  of  volcanic  eruptions,  they  must  be  ancient  forma- 
tions, for  there  is  absolutely  no  evidence  of  any  present  volcanic 
activity.  Fig.  22  represents  one  of  the  finest  lunar  craters,  Gassendi, 
which  is  best  seen  about  two  days  after  the  half  moon. 

154.  Other  Lunar  Formations.  —  The  craters  and  mountains 
are  not  the  only  interesting  features  on  the  moon's  surface. 
There  are  many  deep,  narrow,  crooked  valleys  which  go  by  the 
name  of  "rills/'  and 
may  once  have  been 
water-courses  (see  Fig. 
23).  Then  there  are 
many  straight  "clefts  " 
half  a  mile  or  so  wide, 
and  of  unknown  depth, 
running  in  some  cases 
several  hundred  miles 
straight  through  moun- 
tain and  valley,  with- 
out any  apparent  re- 
gard for  the  accidents 
of  the  surface. 

Most  curious  of  all 
are  the  light-colored 
streaks,  or  "rays," 
which  radiate  from  cer- 
tain of  the  craters,  ex- 
tending in  some  cases 
a  distance  of  many  hundred  miles.  They  are  usually  from  five 
to  ten  miles  wide,  and  neither  elevated  nor  depressed  to  any 
considerable  extent  with  reference  to  the  general  surface. 
Like  the  clefts,  they  pass  across  valley  and  mountain,  and 
sometimes  straight  through  craters,  without  any  change  in 
width  or  color.  No  satisfactory  explanation  of  them  has  yet 


FIG.  23. —  Archimedes  and  the  Apennines  (Nasmyth). 


108 


MAP   OF   THE   MOON. 


[§154 


been  given.  The  most  remarkable  of  these  "  ray-systems  "  is 
the  one  connected  with  the  great  crater  Tycho,  not  very  far 
from  the  moon's  south  pole.  The  rays  are  not  very  conspic- 
uous until  within  a  few  days  of  full  moon,  but  at  that  time 
they,  and  the  crater  from  which  they  diverge,  constitute  by 
far  the  most  striking  feature  of  the  telescopic  view. 


FIG.  24. —  Map  of  the  Moon,  reduced  from  Nelson. 

155.  Changes  on  the  Moon. — It  is  certain  that  there  are 
no  conspicuous  changes  on  the  moon's  surface ;  no  such  trans- 
formations as  would  be  presented  by  the  earth  viewed  with  a 
telescope  from  the  moon,  —  no  clouds,  no  storms,  no  snow  of 


§  155]  CHANGES    ON   THE   MOON.  109 

winter,  and  110  spread  of  verdure  in  the  spring.  At  the  same 
time  it  is  confidently  maintained  by  some  observers  that  here 
and  there  alterations  do  take  place  in  the  details  of  the  lunar 
surface,  while  others  as  stoutly  dispute  it.  The  difficulty  in 
settling  the  question  arises  from  the  great  changes  which  take 
place  in  the  appearance  of  a  lunar  object,  according  to 'the 
angle  at  which  the  sunlight  strikes  it.  Other  conditions  also, 
such  as  the  height  of  the  moon  above  the  horizon  and  the 
clearness  and  steadiness  of  the  air,  affect  the  appearance ;  and 
it  is  very  difficult  to  secure  a  sufficient  identity  of  conditions 
at  different  times  of  observation  to  be  sure  that  apparent 
changes  are  real.  It  is  probable  that  the  question  will  finally 
be  settled  by  photography.  For  further  discussion  of  this 
subject,  see  General  Astronomy,  Art.  272. 

KEY  TO   THE  PRINCIPAL  OBJECTS  INDICATED  IN  FIG.  24. 

A.  Mare  Humorum.  K.  Mare  Nubium. 

B.  Mare  Nectaris.  L.  Mare  Frigoris. 

C.  Oceanus  Procellarum.  T.  Leibnitz  Mountains. 

D.  Mare  Fecunditatis.  U.  Doerfel  Mountains. 

E.  Mare  Tranquilitatis.  V.  Rook  Mountains. 

F.  Mare  Crisium.  W.  D'Alembert  Mountains. 

G.  Mare  Serenitatis.  X.  Apennines. 
//.  Mare  Imbrium.  Y.  Caucasus. 

/.  Sinus  Iridum.  Z.  Alps. 

1.  Clavius.  14.  Alphonsus.  27.  Eratosthenes, 

2.  Schiller.  15.  Theophilus.  28.  Proclus. 

3.  Maginus.  16.  Ptolemy.  28'.  Pliny. 

4.  Schickard.  17.  Langrenus.  29.  Aristarchus. 

5.  Tycho.  18.  Hipparchus.  30.  Herodotus. 

6.  Walther.  19.  Grimaldi.  31.  Archimedes. 

7.  Purbach.  20.  Flam  steed.  32.  Cleomedes. 

8.  Petavius.  21.  Messier.  33.  Aristillus. 

9.  "The  Railway."  22.  Maskelyne.  34.  Eudoxus. 

10.  Arzachel.  23.  Triesnecker.  35.  Plato. 

11.  Gassendi.  24.  Kepler.  36.  Aristotle. 

12.  Catherina.  25.  Copernicus.  37.  Endymion. 

13.  Cyrillus.  26.  Stadius. 


110  NOMENCLATURE.  [§156 

156.  Lunar  Maps  and  Nomenclature. — A  number  of  maps 
of  the  moon  have  been  constructed  by  different  observers. 
The  most  recent  and  extensive  is  that  by  Schmidt  of  Athens, 
on  a  scale  of  seven  feet  in  diameter ;  it  was  published  by  the 
Prussian  government  in  1878.  Perhaps  the  best  for  ordinary 
observers  is  that  given  in  Webb's  "  Celestial  Objects  for  Com- 
mon Telescopes."  We  present  here  (Fig.  24)  a  skeleton  map, 
which  indicates  the  position  of  about  fifty  of  the  leading 
objects. 

As  for  the  names  of  the  lunar  objects,  the  great  plains  upon 
the  surface  were  called  by  Galileo  "  oceans,"  or  "  seas  "  (Maria), 
because  he  supposed  that  these  grayish  surfaces,  which  are 
visible  to  the  naked  eye  and  conspicuous  in  a  small  telescope, 
though  not  with  a  large  one,  were  covered  with  water.  Thus  we 
have  the  "Oceanus  Procellarum"  (Sea  of  Storms),  the  "Mare 
Imbrium"  (Sea  of  Showers),  etc.  The  ten  mountain  ranges 
on  the  moon  are  mostly  named  for  terrestrial  mountains,  as 
Caucasus,  Alps,  Apennines,  though  two  or  three  bear  the 
names  of  astronomers,  like  Leibnitz,  Doerfel,  etc.  The  con- 
spicuous craters  bear  the  names  of  ancient  and  mediaeval 
astronomers  and  philosophers,  as  Plato,  Archimedes,  Tycho, 
Copernicus,  Kepler,  and  Gassendi.  This  system  of  nomencla- 
ture seems  to  have  originated  with  Kiccioli,  who  made  the  first 
map  of  the  moon  in  1650. 


§  157]  THE   SUN.  Ill 


CHAPTER   VI. 

THE  SUN.  —  ITS  DISTANCE,  DIMENSIONS,  MASS,  AND  DEN- 
SITY. —  ITS  ROTATION,  SURFACE,  AND  SPOTS.  —  THE 
SPECTROSCOPE  AND  THE  CHEMICAL  CONSTITUTION  OF 
THE  SUN.  —  THE  CHROMOSPHERE  AND  PROMINENCES. 
—  THE  CORONA. — THE  SUN'S  LIGHT. — MEASUREMENT 
AND  INTENSITY  OF  THE  SUN'S  HEAT.  —  THEORY  OF  ITS 
MAINTENANCE  AND  SPECULATIONS  REGARDING  THE 
AGE  OF  THE  SUN. 

157.  THE  sun  is  a  star, — the  nearest  of  them;  a  hot,  self- 
luminous  globe,   enormous  as  compared  with  the  earth  and 
moon,  though  probably  only  of  medium  size  as  a  star ;  but  to 
the  earth  and  the  other  planets  which  circle  around  it,  it  is 
the  grandest  and  most  important  of  all  the  heavenly  bodies. 
Its  attraction  controls  their  motions,  and  its  rays  supply  the 
energy  which  maintains  every  form  of   activity  upon   their 
surfaces. 

158.  The  Sun's  Distance.  —  The  mean  distance  of  the  sun 
from  the  earth  (the  astronomical  unit  of  distance)  is  a  little 
less  than  93,000000  miles.     There  are  many  methods  of  deter- 
mining it,  some  of  which  depend  on  a  knowledge  of  the  Ve- 
locity of  Light   (Appendix,  Arts.  434  and  436),  while  others 
depend   on   finding   the   sun's   horizontal   parallax.       (For   a 
resumt  of  the  subject,  see  General  Astronomy,  Chap.  XIV.) 
The  mean  value  of  this  parallax  is  very  nearly  8  ".8.     In  other 
words,  as  seen  from  the  sun,  the  earth  has  an  apparent  diam- 
eter of  about  17".6  (Art.  139).     The  distance  is  variable,  to 


112  DIMENSIONS   OF  THE   SUN.  [§  158 

the  extent  of  about  1,500000  miles,  on  account  of  the  eccen- 
tricity of  the  earth's  orbit,  the  earth  being  almost  3,000000 
miles  nearer  to  the  sun  on  Dec.  31st  than  on  July  1st. 

Knowing  the  distance  of  the  earth  from  the  sun,  the  earth's 
orbital  velocity  follows  at  once  by  dividing  the  circumference 
of  the  orbit  by  the  number  of  seconds  in  a  year.  It  comes  out 
18.5  miles  per  second.  (Compare  this  with  the  velocity  of  a 
cannon-ball,  which  seldom  exceeds  2000  feet  per  second.)  In 
travelling  this  18|-  miles,  the  deflection  of  the  earth's  motion  from 
a  perfectly  straight  line  amounts  to  less  than  one-ninth  of  an  inch. 

159.  The  distance  of  the  sun  is  of  course  enormous  compared  with 
any  distance  upon  the  earth's  surface.     Perhaps  the  simplest  illustra- 
tion which  will  give  us  any  conception  of  it  is  that  drawn  from  the 
motion   of  a  railway  train,  which,  going  a  thousand    miles   a  day 
(nearly  forty-two  miles  an  hour  without  stops)  would  take  254i  years 
to  make  the  journey.      If  sound  were  transmitted  through  interplan- 
etary space,  and  at  the  same  rate  as  in  our  own  air,  it  would  make  the 
passage  in  about  fourteen  years ;  i.e.,  an  explosion  on  the  sun  would 
be  heard  by  us  fourteen  years  after  it  actually  occurred.     Light  trav- 
erses the  distance  in  499  seconds. 

160.  Dimensions  of  the  Sun.  —  The   sun's   mean  apparent 
diameter  is  33'  4".     Since  at  its  distance,  1"  equals  450.36 
miles,  its  diameter  is  866,500  miles,  or  109|-  times  that  of  the 
earth.     If  we  suppose  the  sun  to  be  hollowed   out,  and  the 
earth  placed  at  the  centre  of  it,  the  sun's  surface  would  be 
433,000  miles  away.     Now  since   the   distance  of  the  moon 
from   the   earth  is   about  239,000  miles,  she  would  be  only 
a  little  more  than  half-way  out  from  the  earth  to  the  inner 
surface  of  the  hollow  globe,  which  would  thus  form  a  very 
good  background  for  the  study  of  the  lunar  motions. 

If  we  represent  the  sun  by  a  globe  two  feet  in  diameter,  the  earth  on 
the  same  scale  would  be  0.22  of  an  inch  in  diameter,  the  size  of  a  very 
small  pea.  Its  distance  from  the  sun  would  be  just  about  220  feet, 
and  the  nearest  star,  still  on  the  same  scale,  would  be  8000  miles  away, 
on  the  other  side  of  the  earth. 


§  160]  SUN'S   MASS,   DENSITY,   ETC.  113 

Since  the  surfaces  of  globes  are  proportional  to  the  squares 
of  their  radii,  the  surface  of  the  sun  exceeds  that  of  the  earth 
in  the  ratio  of  (109.5)2: 1 ;  i.e.,  the  area  of  its  surface  is  about 
12,000  times  the  surface  of  the  earth. 

The  volumes  of  spheres  are  proportional  to  the  cubes  of 
their  radii,  hence  the  sun's  volume  or  bulk  is  (109.5)3,  or 
1,300000  times  that  of  the  earth. 

161.  The  Sun's  Mass,  Density,  and  Superficial  Gravity.— 

The  mass  of  the  sun  is  nearly  332,000  times  that  of  the  earth. 
There  are  various  ways  of  getting  at  this  result,  but  they  lie 
rather  beyond  the  mathematical  scope  of  this  work. 

Its  density,  as  compared  with  that  of  the  earth,  is  found  by 
simply  dividing  its  mass  by  its  bulk  (both  as  compared  with  the 

ooo  C\C)C\ 

earth);    i.e.,   the   sun's   density  equals          '     -  =  0.255,  —  a 

1,300000 

little  more  than  a  quarter  of  the  earth's  density. 

To  get  its  'specific  gravity'  (i.e.,  its  density  compared  with 
water),  we  must  multiply  this  by  the  earth's  mean  specific 
gravity,  5.58.  This  gives  1.41.  In  other  words,  the  sun's 
mean  density  is  only  about  1.4  times  that  of  water,  a  very 
significant  result  as  bearing  on  its  physical  condition,  espe- 
cially when  we  know  that  a  considerable  portion  of  its  mass  is 
composed  of  metals. 

Of  course  this  low  density  depends  upon  the  fact  that  the  tempera- 
ture is  enormously  high,  and  the  materials  are  mainly  in  a  state  of 
cloud,  vapor,  or  gas. 

The  superficial  gravity  is  about  27.6  as  great  as  gravity  on 
the  earth ;  that  is  to  say,  a  body  which  weighs  one  pound  on 
the  surface  of  the  earth  would  there  weigh  27.6  pounds,  and 
a  person  who  weighs  150  pounds  here  would  there  weigh 
nearly  two  tons.  A  body  would  fall  444  feet  in  the  first 
second,  and  a  pendulum  which  vibrates  seconds  on  the  earth 
would  vibrate  in  less  than  a  fifth  of  a  second  there. 


114 


THE    SUN  S    ROTATION. 


[§162 


162.    The   Sun's   Rotation.  —  Dark   spots   are   often   visible 
upon  the  sun's  surface,  which  pass  across  the  disc  from  east 

to  west  and  indicate  an  axial 
rotation.  The  average  time 
occupied  by  a  spot  in  passing 
around  the  sun  and  return- 
ing to  the  same  apparent  po- 
sition, as  seen  from  the  earth, 
is  27.25  days.  This  interval, 
however,  is  not  the  true  time 
of  the  sun's  rotation,  but  the 
synodic,  as  is  evident  from 
Fig.  25.  Suppose  an  obser- 
ver on  the  earth  at  E  sees  a 
spot  on  the  centre  of  the 


E' 


FIG.  25. 


Synodic  and  Sidereal  Revolutions  of  the  Sun.   sun's    disc    at    S  ',    while    the 

sun  rotates,  E  will  also  move  forward  in  its  orbit,  and  the 
observer,  the  next  time  he  sees  the  spot  on  the  centre  of  the 
disc,  will  be  at  E',  the  spot  having  gone  around  the  whole 
circumference  plus  the  arc  SS'. 

The  equation  by  which  the  true  period  is  deduced  from  the  synodic 
is  the  same  as  in  the  case  of  the  moon ;  viz., 

!=:!_   1 

S      T     E' 

T  being  the  true  period  of  the  sun's  rotation,  E  the  length  of  the  year, 
and  S  the  observed  synodic  rotation.  This  gives  !T=25.35.  Differ- 
ent observers  get  slightly  different  results. 

The  paths  of  the  spots  across  the  sun's  disc  are  usually  more 
or  less  oval,  showing  that  the  sun's  axis  is  inclined  to  the 
ecliptic,  and  so  inclined  that  the  north  pole  is  tipped  about 
7^°  towards  the  position  which  the  earth  occupies  near  the 
first  of  September.  Twice  a  year  the  paths  become  straight, 
when  the  earth  is  in  the  plane  of  the  sun's  equator,  June  3d 
and  Dec.  5th  (Fig.  26). 


§  163]  LAW    OF    THE   SUN'S    ROTATION.  115 

163.   Peculiar  Law  of  the  Sun's  Rotation.  —  It  was  noticed 
quite  early  that  different  spots  give  different  results  for  the 


DEC.  MARCH.  JUNE.  SEPT. 

FIG.  26.  —  Path  of  Spots  across  the  Sun's  Disc. 

period  of  rotation,  but  the  researches  of  Carrington,  about 
thirty  years  ago,  first  brought  out  the  fact  that  the  differences 
are  systematic,  so  that  at  the  solar  equator  the  time  of  solar 
rotation  is  less  than  on  either  side  of  it.  For  spots  near  the 
sun's  equator  it  is  about  25  days ;  for  solar  latitude  30°, 
26.5  days ;  and  in  solar  latitude  40°,  27  days.  The  time  of 
rotation  of  the  sun's  surface  in  latitude  45°  is  fully  two  days 
longer  than  at  the  equator ;  but  we  are  unable  to  follow  the 
law  further  towards  the  poles  of  the  sun,  because  spots  are 
almost  never  found  beyond  the  parallel  of  45°.  No  really 
satisfactory  explanation  of  this  strange  acceleration  of  the 
spots  at  the  sun's  equator  has  yet  been  found. 

164.  Study  of  the  Sun's  Surface.  —  The  heat  and  light  of 
the  sun  are  so  intense  that  we  cannot  look  directly  at  it  with 
a  telescope,  as  we  do  at  the  moon, 
and  it  is  necessary,  therefore,  to 
provide  either  a  special  eye-piece 
with  suitable  shade-glass,  or  arrange 
the  telescope,  as  in  Fig.  27,  so  as  to 
throw  an  image  of  the  sun  upon  a 
screen. 

In  the  study  of  the  sun's  surface, 

photography    is    for    Some    purposes       FIG.  27. -Telescope  and  Screen. 

very  advantageous  and  much  used.  The  instrument  must, 
however,  have  lenses  specially  constructed  for  photographic 


116 


GREAT    SUN    SPOT. 


[§164 


operations,  since  an  object-glass  which  would  give  admirable 
results  for  visual  purposes  would  be  worthless   photograph- 


FIG.  28.— The  Great  Sun  Spot  of  September,  1870,  and  the  Structure  of  the  Photo- 
sphere. From  a  Drawing  by  Professor  Langley.  From  the  "  New  Astronomy  "  by 
permission  of  the  Publishers. 

ically.     The  exposure  required  to  form  a  photographic  picture 
is  practically  instantaneous.     The  negatives  are  usually  from 


§  164]  THE   PHOTOSPHERE.  117 

two  inches  up  to  eight  or  ten  inches  in  diameter,  and  some 
of  the  best  of  them  bear  enlarging  up  to  forty  inches. 

Photographs  have  the  great  advantage  of  freedom  from  preposses- 
sion on  the  part  of  the  observer,  and  in  an  instant  of  time  they  secure 
a  picture  of  the  whole  surface  of  the  sun  such  as  would  require  a  skil- 
ful draughtsman  hours  to  copy.  But,  on  the  other  hand,  they  take  no 
advantage  of  the  instants  of  fine  seeing,  but  represent  the  solar  sur- 
face as  it  happened  to  appear  at  the  moment  when  the  plate  was 
uncovered,  affected  by  all  the  momentary  distortions  due  to  atmos- 
pheric disturbances. 

165.  The  Photosphere.  —  The  sun's  surface  seen  with  a  tele- 
scope, under  a  medium  magnifying  power,  appears  to  be  of 
nearly  uniform  texture,  though  distinctly  darker  at  the  edges, 
and  usually  marked  here  and  there  with  certain  dark  spots. 
With  a  higher  power  it  is  evident  that  the  visible  surface 
(called  the  photosphere)  is  by  no  means  uniform,  but  is  made 
up,  as  shown  in  Fig.  28,  of  a  comparatively  darkish  background 
sprinkled  over  with  grains,  or  "nodules,"  as  Herschel  calls 
them,  of  something  more  brilliant,  —  "like  snowflakes  on  a 
gray  cloth,"  according  to  Langley.  These  nodules  or  "  rice- 
grains"  are  from  400  to  600  miles  across,  and,  when  the  seeing 
is  best,  themselves  break  up  into  more  minute  "granules."  For 
the  most  part,  the  nodules  are  about  as  broad  as  they  are  long, 
though  of  irregular  form;  but  here  and  there,  especially  in 
the  neighborhood  of  the  spots,  they  are  drawn  out  into  long 
streaks,  known  as  "filaments,"  "willow  leaves,"  or  "thatch 
straws." 

Certain  bright  streaks  called  "  f aculse  "  are  also  usually  visi- 
ble here  and  there  upon  the  sun's  surface,  and  though  not  very 
obvious  near  the  centre  of  the  disc,  they  become  conspicuous 
near  the  "  limb,"  or  edge  of  the  disc,  especially  in  the  neigh- 
borhood of  the  spots,  as  shown  in  Fig.  29.  These  faculae  are 
masses  of  the  same  material  as  the  rest  of  the  photosphere, 
but  elevated  above  the  general  level  and  intensified  in  bright- 


118  THE   PHOTOSPHERE.  [§  165 

ness.     When  one  of  them  passes  off  the  edge  of  the  disc,  it  is 
sometimes  seen  as  a  little  projection. 

In  their  nature,  the  photospheric  "nodules  "  and  faculae  are 
in  all  probability  luminous  clouds,  floating  in  a  less  luminous 
atmosphere,  just  as  a  snow  or  rain-cloud,  which  has  been 


FIG.  29.  —  Faculse  at  Edge  of  the  Sun  (De  La  Rue). 

formed  by  the  condensation  of  water-vapor,  floats  in  the  earth's 
atmosphere.  Such  a  cloud,  while  at  a  temperature  even  lower 
than  that  of  the  surrounding  gases,  has  a  vastly  greater  power 
of  emitting  light,  and  therefore  appears  very  brilliant  in  com- 
parison with  the  gas  in  which  it  floats. 

166,  Sun  Spots,  —  Sun  spots,  whenever  visible,  are  the  most 
interesting  and  conspicuous  objects  upon  the  solar  surface. 
The  appearance  of  a  normal  sun  spot  (Fig.  30),  fully  formed 
and  not  yet  beginning  to  break  up,  is  that  of  a  dark  central 
"umbra,"  more  or  less  circular,  with  a  fringing  "penumbra" 
composed  of  converging  filaments.  The  umbra  itself  is  not 
uniformly  dark  throughout,  but  is  overlaid  with  filmy  clouds, 


166] 


SUN   SPOTS. 


119 


which  usually  are  rather  hard  to  see,  but  sometimes  are  con- 
spicuous, as  in  the  figure.  Usually,  also,  within  the  umbra 
there  are  a  number  of  round  and  very  black  spots,  sometimes 
called  "vortices,"  but  often  referred  to  as  "  Dawes's  holes," 
after  the  name  of  their  first  discoverer. 

Even  the  darkest  portions  of  the  umbra,  however,  are  dark 
only  by  contrast.      Photometric   observations   show   that  the 


FIG.  30.  — A  Normal  Sun  Spot  (Secchi;  modified). 

nucleus  of  a  spot  gives  about  one  per  cent  as  much  light  as 
a  corresponding  area  of  the  photosphere ;  the  blackest  portion 
of  a  sun  spot  is  really  more  brilliant  than  a  calcium  light. 

Very  few  spots  are  strictly  normal.  Frequently  the  umbra 
is  out  of  the  centre  of  the  penumbra,  or  has  a  penumbra  on 
one  side  only,  and  the  penumbral  filaments,  instead  of  con- 
verging regularly  towards  the  nucleus,  are  often  distorted  in 
every  conceivable  way.  Spots  are  often  gathered  in  groups 
within  a  common  penumbra,  separated  from  each  other  by 
brilliant  "bridges,"  which  extend  across  from  the  outside 


120  SUN   SPOTS.  [§  166 

photosphere.  Occasionally  a  spot  has  no  penumbra  at  all,  and 
sometimes  we  have  what  are  called  "  veiled  "  spots,  in  which 
there  seems  to  be  a  penumbra  without  any  central  nucleus. 

167.  Nature  of  Sun  Spots.  —  The  spots  are  unquestionably 
cavities  or  hollows  in  the  photosphere,  and  are  filled  with  gases 
and  vapors  which  are  cooler  than  the  surrounding  regions,  and 
therefore  absorb  a  considerable  portion  of  light,  and  make  the 
spot  look  dark.  The  fact  that  they  are  depressions  is  shown 
by  the  change  in  their  appearance  as  they  approach  the 
"limb"  of  the  disc.  Here  the  penumbra  becomes  wider  on 
the  outer  edge,  and  narrower  on  the  inner  edge,  and  just  before 
the  spot  goes  out  of  sight  around  the  edge  of  the  sun,  the 
penumbra  on  the  inner  edge  entirely  disappears.  The  appear- 
ance is  precisely  such  as  would  be  shown  by  a  saucer-shaped 


FIG.  31.  —  Sun  Spots  as  Cavities. 

cavity  in  the  surface  of  a  globe,  the  bottom  of  the  cavity  being 
painted  black  to  represent  the  umbra,  and  the  sloping  sides 
gray  for  the  penumbra  (see  Fig.  31). 

Observations  upon  a  single  spot  would  hardly  be  sufficient  to  prove 
this,  because  the  spots  are  so  irregular  in  their  form ;  but  by  observ- 
ing the  behavior  of  several  hundred,  the  truth  comes  out  clearly. 
Occasionally  when  a  very  large  spot  passes  off  the  sun's  limb,  the 
depression  can  be  seen  with  the  telescope. 

That  the  nucleus  of  a  spot  is  cooler  as  well  as  darker  than 
the  rest  of  the  sun's  surface,  has  been  proved  by  several 
observers  by  direct  experiments. 


§  167]  DIMENSIONS    OF   SUN   SPOTS.  121 

The  penumbra  is  usually  composed  of  "  thatch  straws/7  or 
long  drawn  out  filaments,  and  these,  as  has  been  said,  con- 
verge in  a  general  way  towards  the  centre  of  the  spot.  In  the 
neighborhood  of  the  spot,  the  surrounding  photosphere  is 
usually  much  disturbed  and  elevated  into  faculse. 

168.  Dimensions  of  Sun  Spots,  etc.  —  The  diameter  of  the 
umbra  of  a  sun  spot  varies  all  the  way  from  500  miles,  in  the 
case  of  a  very  small  one,  to  50,000  miles  in  the  case  of  a  very 
large   one.      The  penumbra  surrounding  a  group  of   spots  is 
sometimes  150,000  miles  across,  though  that  is  an  exceptional 
size.     Quite  frequently  sun  spots  are  large  enough  to  be  visi- 
ble with  the  naked  eye,  and  can  actually  be  thus  seen  at  sun- 
set or  through  a  fog,  or  by  the  help  of  a  simple  colored  glass. 
The  depth  of  the  bottom  of  a  spot  is  very  difficult  to  deter- 
mine, but  according  to  Faye,  Carrington,  and  some  others,  it 
seldom  exceeds  2500  miles,  and  more  often  is  between  500  and 
1500. 

The  duration  of  sun  spots  is  very  various,  but  they  are 
always  short-lived  phenomena  from  the  astronomical  point  of 
view,  sometimes  lasting  only  for  a  few  days,  though  more  fre- 
quently for  a  month  or  two.  In  one  instance  a  spot  group 
attained  the  age  of  eighteen  months. 

Very  little  can  be  said  as  to  their  cause.  Numerous  theo- 
ries, more  or  less  satisfactory,  have  been  proposed.  On  the 
whole,  perhaps  the  most  probable  view  is  that, they  are  the 
effect  of  eruptions.  It  is  not  likely,  however,  that  they  are 
the  holes  or  craters  through  which  the  eruptions  break  out,  as 
Secchi  at  one  time  thought,  and  as  Mr.  Proctor  maintained  to 
the  very  last :  it  is  more  probable,  in  accordance  with  Secchi' s 
later  views,  that  when  an  eruption  takes  place,  a  hollow,  or 
sink,  results  in  the  photospheric  cloud-surface  somewhere  near 
it,  in  which  hollow  the  cooler  gases  and  vapors  collect. 

169.  Distribution  of  Spots,  and  their  Periodicity. — It  is  a 

significant  fact  that  the  spots  are  confined  mostly  to  two  zones 


122  INFLUENCE   OF   SUN    SPOTS.  [§  169 

of  the  sun's  surface  between  5°  and  40°  of  north  and  south 
solar  latitude.  Practically  none  are  ever  found  beyond  the 
latitude  of  45°,  but  at  the  time  when  spots  are  most  numerous, 
a  few  are  found  near  the  equator.  In  1843  Schwabe  of  Dessau, 
by  the  comparison  of  an  extensive  series  of  observations  cover- 
ing nearly  twenty  years,  showed  that  the  sun  spots  are  probably 
periodic,  being  at  some  times  much  more  numerous  than  at 
others,  with  a  roughly  regular  recurrence  every  ten  or  eleven 
years.  A  few  years  later  he  fully  established  this  remarkable 
result.  Wolf  of  Zurich  has  collected  all  the  observations  dis- 
coverable, and  has  obtained  a  pretty  complete  record  back  to 
1610,  when  Galileo  first  discovered  these  objects.  The  aver- 
age period  is  11.1  years,  but  the  maxima  are  somewhat  irregu- 
lar, both  in  time  and  as  to  the  extent  of  the  surface  covered 
by  spots.  The  last  maximum  occurred  in  1883-4.  During 
the  maximum  the  sun  is  never  free  from  spots,  from  25  to  50 
being  frequently  visible  at  once.  During  the  minimum,  on  the 
contrary,  weeks  and  even  months  pass  without  the  appearance 
of  even  a  single  one.  The  cause  of  this  periodicity  is  not  yet 
known. 

170.  Terrestrial  Influence  of  Sun  Spots.  —  One  influence  of 
sun  spots  on  the  earth  is  perfectly  demonstrated.  When  the 
spots  are  numerous,  magnetic  disturbances  (magnetic  storms) 
are  most  numerous  and  most  violent  upon  the  earth — a  fact  not 
to  be  wondered  at,  since  notable  disturbances  upon  the  sun's 
surface  have  been  immediately  followed  by  magnetic  storms 
with  brilliant  exhibitions  of  the  Aurora  Borealis,  as  in  1859 
and  1883.  But  no  one  has  yet  been  able  to  explain  the  nature 
of  the  connection  by  which  disturbances  upon  the  sun's  sur- 
face affect  the  magnetic  condition  of  the  earth,  though  the  fact 
is  beyond  doubt. 

It  has  been  attempted,  also,  to  show  that  the  periodical  disturbance 
of  the  sun's  surface  is  accompanied  by  effects  upon  the  earth's  mete- 
orology, —  upon  its  temperature,  barometric  pressure,  storminess,  and 


§  170]  THE   SOLAR    SPECTRUM.  123 

the  amount  of  rainfall.  On  the  whole,  it  can  only  be  said  that  while 
it  is  possible  that  real  effects  are  produced,  they  must  be  very  slight, 
and  are  almost  entirely  covered  up  by  the  effect  of  purely  terrestrial 
causes.  The  results  obtained  thus  far  in  attempting  to  co-ordinate 
sun-spot  phenomena  with  meteorological  phenomena  are  unsatisfac- 
tory and  often  contradictory.  We  may  add  that  the  spots  cannot 
produce  any  sensible  effect  by  their  direct  action  in  diminishing  the 
light  and  heat  of  the  sun.  They  do  not  directly  alter  the  amount  of 
solar  radiation  at  any  time  by  so  much  as  one  part  in  a  thousand. 

THE   SOLAR   SPECTRUM  AND   ITS  REVELATIONS. 

About  1860  the  spectroscope  appeared  in  the  field  as  a  new 
and  powerful  instrument  for  astronomical  research,  resolving 
at  a  glance  many  problems  which  before  did  not  seem  even 
open  to  investigation. 

171.  Principle  of  the  Spectroscope.  —  The  essential  part  of 
the  apparatus  is  either  a  prism  or  a  train  of  prisms,  or  else  a 
diffraction  "  grating/' *  which  is  capable  of  performing  the 
same  office  of  "  dispersing "  (i.e.,  of  spreading  and  sending  in 
different  directions)  the  light  rays  of  different  colors. 

If  with  such  a  "  dispersion  piece,"  as  we  may  call  it  (either 
prism  or  grating),  one  looks  at  a  distant  point  of  light,  he  will 
see  instead  of  a  point  a  long,  bright  streak,  red  at  one  end  and 
violet  at  the  other.  If  the  object  looked  at  is  a  line  of  light, 
parallel  to  the  edge  of  the  prism  or  to  the  lines  of  the  grating, 
then  instead  of  a  colored  streak  without  width,  he  gets  a 
colored  band  or  ribbon  of  light,  the  spectrum,  which  may  show 
markings  which  will  give  him  much  valuable  information.  It 
is  usual  to  form  this  line  of  light  by  admitting  the  rays 
through  a  narrow  "  slit "  placed  at  one  end  of  a  tube,  which 
carries  at  the  other  end  an  achromatic  object-glass  having 

1  The  "  grating  "  is  merely  a  piece  of  glass  or  speculum  metal,  ruled  with 
many  thousand  straight,  equidistant  lines,  from  5000  to  20,000  in  the 
inch. 


124 


THE   SPECTROSCOPE. 


[§171 


the  slit  in  the  principal  focus.  This  tube,  with  slit  and  lens, 
constitutes  the  "  collimator."  Instead  of  looking  at  the  spec- 
trum with  the  naked  eye,  it  is  better  also  in  most  cases  to  use 
a  small  "  view  telescope,"  so  called  to  distinguish  it  from  the 
large  telescope  to  which  the  spectroscope  is  often  attached. 

172.  Construction  of  the  Spectroscope. — The  instrument, 
therefore,  as  usually  constructed,  and  shown  in  Fig.  32,  con- 
sists of  three  parts,  —  collimator,  dispersion-piece,  and  view 


Prism-Spectroscope 


Grating-Spectroscope 
Collimator  \S2 


Grating 


S, 


Direct-Vision  Spectroscope 
FIG.  32.  —  Different  Forms  of  Spectrum. 

telescope,  —  although  in  the  "direct-vision"  spectroscope, 
shown  in  the  figure,  the  view  telescope  is  omitted.  If  the  slit 
S  be  illuminated  by  strictly  homogeneous  light  (i.e.,  light  all 
of  one  color),  say  yellow,  the  "real  image"  of  the  slit  will  be 
found  at  Y.  If,  at  the  same  time,  light  of  a  different  color 
—  red  for  instance  —  be  also  admitted,  a  second  image  will  be 
formed  at  jR,  and  the  observer  will  then  see  a  spectrum  with 


§  172]  SPECTRUM  ANALYSIS.  125 

two  bright  lines,  the  lines  being  really  nothing  more  than  images 
of  the  slit. 

If  violet  light  be  admitted,  a  third  image  will  be  formed  at 
F,  and  there  will  be  three  bright  lines.  If  light  from  a  candle 
be  admitted,  there  will  be  an  infinite  number  of  these  slit- 
images  close  together,  like  the  pickets  in  a  fence,  without 
interval  or  break,  and  we  then  get  what  is  called  a  i  continu- 
ous ?  spectrum.  If,  however,  we  look  at  sunlight  or  moonlight 
or  the  light  of  a  star,  we  shall  find  a  spectrum  continuous  in 
the  main,  but  crossed  by  numerous  dark  lines,  or  missing  slit- 
images  (as  if  some  of  the  fence-pickets  had  been  knocked  off, 
leaving  gaps). 

173.  Principles  upon  which  Spectrum  Analysis  depends.  — 

These,  substantially,  as  announced  by  Kirchhoff  in  1858,  are 
the  three  following :  — 

1st.  A  continuous  spectrum  is  given  by  bodies  which  are  so 
dense  that  the  molecules  interfere  with  each  other  in  such  a 
way  as  to  prevent  their  free  vibration ;  i.e.,  by  bodies  which 
are  either  solid  or  liquid,  or,  if  gaseous,  are  under  pressure. 

2d.  The  spectrum  of  a  luminous  gas  under  low  pressure  is 
discontinuous,  that  is,  it  is  made  up  of  bright  lines  or  bands,  and 
these  lines  are  characteristic.  The  same  substance  under  simi- 
lar conditions  always  gives  the  same  set  of  lines,  and  usually 
it  does  so  even  under  conditions  which  differ  rather  widely ; 
but  when  the  circumstances  differ  too  much,  it  may  give  two 
or  more  different  spectra. 

3d  (and  most  important  for  our  purpose  just  now).  A  gas  or 
vapor  absorbs  from  a  beam  of  white  light  passing  through  it 
precisely  those  rays  of  which  its  own  spectrum  consists;  so  that 
the  spectrum  of  white  light  which  has  been  transmitted 
through  such  a  vapor,  if  the  vapor  is  cooler  than  the  original 
source  of  light,  exhibits  a  "  reversed  "  spectrum  of  the  gas ; 
i.e.,  we  get  a  spectrum  which  shows  dark  lines  in  place  of  the 
characteristic  bright  lines. 


126 


SPECTRUM  ANALYSIS. 


[§173 


We  therefore  infer  that  the  sun  is  covered  by  an  envelope 
of  gases,  not  so  hot  as  the  luminous  clouds  which  form  the 
photosphere,  and  that  these  gases  by  their  absorption  produce 
the  dark  lines  which  we  see. 

174.   Experiment  illustrating  Reversal  of  Spectrum.  —  The 

principle  of  reversal  is  illustrated  by  Fig.  33.     Suppose  that 
in  front  of  the  spectroscope  we  place  a  spirit  lamp  with  a  little 


FIG.  33.  —  Reversal  of  the  Spectrum. 

carbonate  of  soda  and  some  salt  of  thallium  upon  the  wick. 
We  shall  then  get  a  spectrum  showing  the  two  yellow  lines  of 
sodium  and  the  green  line  of  thallium,  all  bright,  as  in  the 
upper  of  the  two  spectra.  If  now  the  liine  light  be  started 
behind  the  flame,  we  shall  at  once  get  the  effect  shown  in  the 
lower  figure,  —  a  continuous  spectrum  crossed  by  three  black 
lines  which  exactly  replace  the  bright  ones.  Thrust  a  screen 
between  the  lamp  flame  and  the  lime,  and  the  dark  lines 
instantly  turn  bright  again. 


175] 


SPECTRUM  ANALYSIS. 


127 


175.   Chemical  Constituents  of   the  Solar  Atmosphere. — By 

taking  advantage  of  these  principles,  we  can  detect  a  large 
number  of  well-known  terrestrial  elements  in  the  sun.  The 
solar  spectrum  is  crossed  by  dark  lines,1  which  with  an  instru- 
ment of  high  power  number  several  thousand. 

By  proper  arrangements  it  is  possible  to  identify  among 
these  lines  many  which  are  due  to  the  presence  in  the  sun's 
atmosphere  of  known  terrestrial  elements  in  the  state  of 
vapor.  To  effect  the  comparison  necessary  for  this  purpose, 
the  spectroscope  must  be  so  arranged  that  the  observer  can 
confront  the  spectrum  of  sunlight  with  that  of  the  substance 
to  be  tested.  In  order  to  do  this,  half  of  the  slit  is  covered 
by  a  little  reflector  or  "  comparison  prism,"  which  reflects  into 
the  tube  the  light  of  the  sun,  while  the  other  half  of  the 
slit  receives  directly  the  light  of  some  flame  or  electric 
spark.  On  looking  into  the  spectroscope,  the  observer  will 
then  see  a  spectrum,  the  lower  half  of  which,  for  instance,  is 


FIG.  34.  —  Comparison  of  the  Spectrum  of  Iron  with  the  Solar  Spectrum.    From  a 
Negative  by  Professor  Trowbridge. 

made  by  sunlight,  while  the  upper  half  is  made  by  light  com- 
ing from  an  electric  spark  between  two  metal  points,  say  of 
iron.  This  latter  spectrum  will  show  the  bright  lines  of  iron 
vapor,  and  the  observer  can  then  easily  see  whether  they  do 
or  do  not  correspond  exactly  with  the  dark  lines  of  the  solar 
spectrum. 

1  They  are  generally  referred  to  as  Fraunhofer's  lines,  because  Fraun- 
hofer  was  the  first  to  map  them.  To  some  of  the  principal  ones  he 
assigned  letters  of  the  alphabet,  which  are  still  retained;  thus  A  is  a 
strong  red  line  at  the  extreme  end  of  the  spectrum ;  C,  one  in  the  scarlet ; 
D,  one  in  the  yellow  ;  and  H,  one  in  the  violet. 


128  THE  CHROMOSPHERE.  [§  175 

In  such  comparisons  photography  may  be  most  effectively  used 
instead  of  the  eye.  Fig.  34  is  a  rather  unsatisfactory  reproduction, 
on  a  reduced  scale,  of  a  negative  made  by  Professor  Trowbridge  of 
Cambridge.  The  lower  half  is  the  violet  portion  of  the  sun's  spec- 
trum, and  the  upper  half  that  of  an  electric  arc  charged  with  the 
vapor  of  iron.1  The  reader  can  see  for  himself  with  what  absolute 
certainty  such  a  photograph  indicates  the  presence  of  iron  in  the  solar 
atmosphere.  A  few  of  the  lines  in  the  photograph  which  do  not  show 
corresponding  lines  in  the  solar  spectrum  are  due  to  impurities  in  the 
carbon,  and  not  to  iron. 

176.   Elements  known  to  exist  in  the  Sun.  —  As  the  result  of 
such  comparisons,  we  have  the  following  list  of  sixteen  ele- 
ments which  are  now  (1890)  known  to  exist  in  the  sun :  — 
Barium,  Manganese, 

Calcium,  Nickel, 

Chromium,  Platinum, 

Cobalt,  Silicon, 

Copper,  Silver, 

Hydrogen,  Sodium, 

Iron,  Titanium, 

Magnesium,  Vanadium. 

There  are  evidences,  perhaps  not  quite  conclusive,  of  the 
presence  of  several  more,  viz.  — 

Aluminium,  Lead(?), 

Cadmium,  Molybdenum  (?), 

Carbon,  Palladium  (?), 

Zinc,  Uranium  (?). 

As  to  carbon,  its  spectrum  is  so  peculiar,  consisting  of  bands 
rather  than  lines,  that  it  is  very  difficult  to  be  sure ;  but  the 
tendency  of  the  latest  investigations  is  to  establish  its  place 
in  the  upper  list.  These  bodies  must,  of  course,  in  the  sun  all 
be  in  a  condition  of  vapor,  and  vapor  somewhat  cooler  than  the 
clouds  which  form  the  photosphere.  It  will  be  noticed  that 

1  Of  course,  in  the  negative,  dark  lines  show  bright,  and  vice  versa. 


§  176]  THE   REVERSING   LAYER.  129 

the  elements  named  in  the  lists,  carbon  alone  excepted,  are 
all  metals  (chemically,  hydrogen  is  as  much  a  metal  as  any  of 
the  others),  and  that  a  number  of  the  elements  which  are  most 
important  in  the  constitution  of  the  earth's  surface  fail  to 
appear.  As  yet  oxygen,  nitrogen,  chlorine,  bromine,  iodine, 
sulphur,  phosphorus,  and  boron  are  all  missing. 

We  must  be  cautious,  however,  in  drawing  negative  con- 
clusions. It  is  quite  conceivable  that  the  spectra  of  these 
bodies  in  their  solar  conditions  may  be  so  different  from  their 
spectra  as  presented  in  our  laboratories,  that  we  cannot  easily 
recognize  them ;  for  it  is  now  unquestionable  that  many  sub- 
stances, under  different  conditions,  give  two  or  more  widely 
differing  spectra. 

177.  The  Reversing  Layer.  —  According  to  Kirchhoff's  theory 
the  dark  lines  are  formed  by  the  passing  of  light  emitted  by 
minute  solid  or  liquid  particles  of  photospheric  clouds  through 
the  somewhat  cooler  vapors  which  compose  the  substances 
that  we  recognize  by  the  dark  lines  in  the  spectrum.  If  this 
is  so,  the  spectrum  of  the  gaseous  envelope,  which  by  its 
absorption  forms  the  dark  lines,  ought  to  show  a  spectrum  of 
corresponding  bright  lines  when  seen  by  itself.  The  oppor- 
tunities are  rare  when  it  is  possible  to  obtain  a  spectrum  of 
this  gaseous  envelope  separate  from  that  of  the  photosphere ; 
but  at  the  time  of  a  total  eclipse,  at  the  moment  when  the 
sun's  disc  has  just  been  obscured  by  the  moon,  and  the  sun's 
atmosphere  is  still  visible  beyond  the  moon's  limb,  the  ob- 
server ought  to  see  this  bright-line  spectrum,  if  the  slit  of  the 
spectroscope  be  carefully  directed  to  the  proper  point ;  land  the 
observation  has  actually  been  made.  The  lines  of  the  solar 
spectrum,  which  up  to  the  time  of  the  total  obscuration  of  the 
sun  remain  dark  as  usual,  are  suddenly  reversed,  and  the  whole 
field  of  the  spectroscope  is  filled  with  brilliant  colored  lines, 
which  flash  out  quickly,  and  then  gradually  fade  away,  disap- 
pearing in  about  two  seconds. 


130 


SUN-SPOT   SPECTRUM. 


The  natural  interpretation  of  this  phenomenon  is  that  the 
formation  of  the  dark  lines  in  the  solar  spectrum  is,  mainly  at 
least,  produced  by  a  very  thin  stratum  closely  covering  the 
photosphere,  since  the  moon's  motion  in  two  seconds  would 
correspond  to  a  thickness  of  only  500  miles. 

There  are  reasons,  however,  to  doubt  whether  the  lines  are  all 
produced  in  such  a  thin  layer.  According  to  Mr.  Lockyer,  the  solar 
atmosphere  is  very  extensive,  and  certain  lines  of  the  spectrum  appear 
to  be  formed  only  in  the  regions  of  lower  temperature  high  up  above 
the  surface  of  the  photosphere. 

178.  Sun-Spot  Spectrum. — The  spectrum  of  a  sun  spot 
differs  from  the  general  solar  spectrum  not  only  in  its  dimin- 
ished brilliancy,  but  in  the  great  widening  of  certain  lines,  the 
thinning  of  others,  and  the  change  of  some  (especially  the  lines 
of  hydrogen)  to  bright  lines  on  some  occasions.  The  majority 
of  the  Fraunhofer  lines,  however,  are  not  much  affected  either 
way. 

Sometimes,  in  connection  with  sun  spots,  certain  lines  of  the 
spectrum  are  bent  and  broken,  as  shown  in  Fig.  35.  These 

distortions  are  explained  by 
the  swift  motion  towards  or 
from  the  observer  of  the 
gaseous  matter,  which  by 
its  absorption  produces  the 
line  in  question.  In  the  case 

2*  43"  2M6°"  2^51-"  .,,  /"    ,    .      ,,       „ 

Pie.  35.  -  The  c  line  in  the  Spectrum  of  a     illustrated  in  the  figure,  hy- 
Sun  Spot.  drogen  was   the    substance, 

and  its  motion  was  towards  the  observer,  nearly  at  the  rate  of 
300  miles  a  second  at  one  point. 


179.  Doppler's  Principle. — The  principle  upon  which  the 
explanation  of  this  displacement  and  distortion  of  lines  de- 
pends was  first  enunciated  by  Doppler  in  1842.  It  is  this: 
when  the  distance  between  us  and  a  body  which  is  emitting  regular 


§  179]  THE  CHROMOSPHERE.  131 

vibrations,  either  of  sound  or  of  light,  is  decreasing,  then  the 
number  of  pulsations  received  by  us  in  each  second  is  increased, 
and  the  length  of  the  tvaves  is  correspondingly  diminished.  Thus 
the  pitch  of  a  musical  tone  rises  in  the  case  supposed,  and  in 
the  same  way  the  refrangibility  of  a  light  wave,  which  depends 
upon  its  wave  length,  is  increased,  so  that  it  will  fall  nearer 
the  violet  end  of  the  spectrum.  This  principle  finds  numerous 
applications  in  modern  astronomical  spectroscopy,  and  it  is  of 
extreme  importance  that  the  student  should  clearly  under- 
stand it. 

180.  The  Chromosphere.  —  Outside  the  photosphere,  or  shin- 
ing surface  of  the  sun,  lies  the  so-called  chromosphere,  of  which 
the  stratum  of  gases  that  produce  the  dark  lines  in  the  solar 
spectrum  is  the  hottest  and  densest  portion.     The  word  is 
derived  from  the  Greek,  chroma  (color),  and  means  "color- 
sphere."     It  is  so-called  because  it  is  brilliantly  scarlet,  owing 
this  color  to  the  hydrogen  gas  which  is  its  most  conspicuous 
component.     In  structure,  it  is  like  a  sea  of  flame,  covering 
the  photosphere  to  a  depth  of  from  5000  to  10,000  miles,  and 
as  seen  through  a  telescope  at  the  time  of  a  total  eclipse,  it 
has  been  well  described  as  looking  like  a  "prairie  on  fire." 
There  is,  however,  no  real  burning  in  the  case ;  i.e.,  no  heat- 
producing  combination  of  hydrogen  with  oxygen,  or  with  any 
other  element. 

Under  ordinary  circumstances  the  chromosphere  is  invisible, 
drowned  in  the  light  of  the  photosphere.  It  can  be  seen  with 
the  telescope  only  for  a  few  seconds  at  a  time,  during  the  fleet- 
ing moments  of  a  total  eclipse ;  but  with  the  spectroscope  it 
can  be  studied  at  other  times,  as  we  shall  see. 

181.  Prominences.  — The  prominences,  or  protuberances,  are 
scarlet  clouds  which  are  seen  during  a  total  eclipse,  projecting 
from  behind  the  edge  of  the  moon.     They  are  simply  exten- 
sions  of  the  chromosphere,  or  isolated  clouds  of  the  same 


132  PROMINENCES  AND   CHROMOSPHERE.  [§  181 

gaseous  substances,  chiefly  hydrogen.  Their  true  nature  was 
first  established  at  an  eclipse  in  1868,  when  their  spectrum 
was  first  satisfactorily  made  out.  This  spectrum  is  com- 
posed of  numerous  bright  lines,  conspicuous  among  which  are 
the  lines  of  hydrogen,  together  with  a  brilliant  yellow  line 
(sometimes  called  D3  because  near  the  two  so-called  D  lines). 
It  is  due  to  some  substance  not  yet  recognized,  but  provision- 
ally called  helium,  that  is,  '  the  metal  of  the  sun/  from  the 
Greek,  helios  (the  sun). 

182.  Spectroscopic  Observations  of  the  Prominences  and  Chro- 
mosphere.—  Since  the  spectrum  of  these  objects  is  composed 
of  a  small  number  of  brilliant  lines,  it  is  possible  to  observe 
them  with  a  spectroscope  in  full  daylight.     The  explanation 
of  the  way  in  which  the  spectroscope  effects  this  lies  rather 
beyond  our  limitations ;  but  it  is  sufficient  for  our  purpose  to 
say  that  by  attaching  a  spectroscope  to  a  good  telescope  the 
prominences  can  now  be  studied  at  leisure  any  clear  day.    They 
are  wonderfully  interesting  and  beautiful  objects.      Some  of 
them,  the  so-called  "  quiescent "  prominences,  are  of  enormous 
size,  50,000  or  even  100,000  miles  in  height,  faint  and  diffuse, 
remaining  almost  unchanged  for  days.     Others  are  much  more 
brilliant  and  active,  especially  those  that  are  associated  with 
sun  spots,  as  many  of  them  are.     These  "eruptive"  promi- 
nences often  alter  their  appearance  very  rapidly,  —  so   fast 
that  one  can  sometimes  actually  see  the  motion:   velocities 
from  50  to  200  miles  a  second  are  frequently  met  with.     As  a 
rule  the  eruptive  prominences  are  not  so  large  as  the  quiescent 
ones,  but  occasionally  they  surpass  them,  and  a  few  have  been 
observed  to  attain   elevations   of  more  than  200,000  miles. 
Fig.  36  gives  specimens  of  both  kinds. 

183.  The  Corona. — Probably  the  most  beautiful  and  im- 
pressive of  all  natural  phenomena  is  the  corona,  the  "  glory  " 
of  light  which  surrounds  the  sun  at  a  total  eclipse.     The  por- 


183] 


THE   CORONA. 


133 


tion  of  it  near  the  sun  is  dazzlingly  bright  and  of  a  pearly 
lustre,  contrasting  beautifully  with  the  scarlet  prominences, 
which  stud  it  like  rubies.  It  seems  to  be  mainly  composed 


Quiescent  Prominences. 


Flames.  Jets  and  Spikes  near  Sun's  Limb,  Oct.  5,  1571. 

%  Eruptive  Prominences. 

FIG.  36. 

of  projecting  filaments  of  light,  which  near  the  sun  are 
pretty  well  defined,  but  at  a  little  distance  fade  out  and  melt 
into  the  general  radiance.  Near  the  poles  of  the  sun  the 
corona  does  not  usually  extend  very  far  and  has  a  pretty 
definite  outline,  but  in  the  spot  regions  and  near  the  sun's 
equator  faint  streams  sometimes  extend  to  a  distance  of  sev- 
eral degrees;  and  at  the  distance  of  the  sun  every  degree 
means  more  than  a  million  of  miles. 

A  very  striking  and  perplexing  feature  is  the  existence  of 


134 


THE   CORONA. 


[§  183 


perfectly  straight  dark  rays  or  rifts,  which  reach  clear  down 

to  the  very  edge  of  the  sun. 

The  corona  varies  very  greatly  in  brightness   at   different 

eclipses,  according  to  the  apparent  diameter  of  the  moon  at 

the  time.  The  portion  of 
the  corona  nearest  the  sun 
is  so  much  brighter  than 
the  outer  regions  that 
a  little  increase  of  the 
moon's  diameter  cuts  off 
a  very  large  proportion  of 
the  light.  The  total  light 
of  the  corona  is  always  at 
least  two  or  three  times 
as  great  as  that  of  the  full 
moon. 

Fig.  37  represents  the 
corona  as  seen  in  the 
eclipse  of  1882. 

184.  Spectrum  of  the 
Corona.  —  A  characteris- 
tic feature  of  its  spectrum 
is  a  bright  green  line, 
generally  known  as  the 
"1474"  line.1  This  line  was  at  first  supposed  to  be  due  to 
iron,  and  the  coincidence  was  for  a  long  time  puzzling  (since 
the  vapor  of  iron  is  a  very  improbable  substance  to  be  found 
at  an  elevation  above  the  hydrogen  of  the  chromosphere),  until 
it  was  discovered  that  the  line  is  really  a  close  double.  One  of 
the  two  components  of  the  dark  line  is  due  to  iron,  while  the 
other,  the  true  corona  line,  is  due  to  some  unknown  gaseous 

1  So-called  because  it  coincides  with  a  dark  line  on  Kirchhoff's  map  of 
the  solar  spectrum,  which  was  the  chart  in  use  when  the  line  was  first 
discovered,  in  1869. 


FIG.  37. 
Corona  of  the  Egyptian  Eclipse,  1882. 


§  184]  THE   CORONA.  135 

element  (probably  lighter  than  hydrogen),  which   has   been 
called  coronium,  after  the  analogy  of  helium. 

Besides  this  conspicuous  green  line,  the  hydrogen  lines  are 
also  faintly  visible  in  the  corona  spectrum ;  and  by  means  of 
photography  it  has  been  found  that  the  violet  and  ultra-violet 
portions  of  the  spectrum  are  also  rich  in  bright  lines,  the  two 
wide  lines  or  bands,  known  as  H  and  K  in  the  ordinary  solar 
spectrum,  being  especially  bright  and  conspicuous. 

185.  The  corona  is_  proved  to  be  a  true  appendage  of  the 
sun,  and  not,  as  has  been  at  times  supposed,  a  mere  optical 
phenomenon,  nor  one  due  to  the  atmosphere  of  the  earth  or 
moon,  by  two  established  facts  :  — 

1st.  That  its  spectrum  is  not  that  of  reflected  sunlight,  but 
of  a  self-luminous  gas  j  and 

2d.  Because  photographs  of  the  corona,  made  at  widely  dif- 
ferent stations  along  the  track  of  an  eclipse,  agree  exactly  in 
details. 

Its  real  nature  and  relation  to  the  sun  is  very  difficult  to 
explain.  It  is  a  gaseous  envelope,  at  least  mainly  gaseous,  as 
our  atmosphere  is,  but  it  does  not  stand  in  any  such  relations 
to  the  globe  beneath  as  does  the  air.  Its  phenomena  are  not 
yet  satisfactorily  explained,  and  remind  us  far  more  of  auroral 
streamers  and  of  comets'  tails  than  of  anything  that  occurs  in 
the  lower  regions  of  the  earth's  atmosphere.  The  material  of 
the  corona  is  of  excessive  rarity,  as  is  shown  by  the  fact  that 
in  a  number  of  cases  comets  have  passed  directly  through  it 
(as,  for  instance,  in  1882)  without  the  slightest  perceptible 
disturbance.  Its  density,  therefore,  must  be  almost  incon- 
ceivably less  than  that  of  the  best  vacuum  which  we  are  able 
to  produce. 

SUN'S  LIGHT   AND  HEAT. 

186.  The  Sun's  Light.  —  By  photometric  measures,  which 
we  cannot  explain  here,  it  is  found  that  the  sun  gives  us  1575 


136  SUN'S   LIGHT   AND   HEAT.  [§  186 

billions  of  billions  (1575  followed  by  24  ciphers)  times  as 
much  light  as  a  standard  candle *  would  do  at  that  distance. 

The  amount  of  light  received  from  the  sun  is  about  600,000 
times  that  given  by  the  full  moon,  about  7000,000000  times 
that  of  Sirius,  the  brightest  of  the  fixed  stars,  and  fully 
200,000,000000  times  that  of  the  Pole-star.  As  to  the  inten- 
sity of  sunlight,  or  the  intrinsic  brightness  of  the  sun's  sur- 
face, we  find  that  it  is  about  190,000  times  as  bright  as  that 
of  the  candle  flame,  and  fully  150  times  as  bright  as  the  lime 
of  a  calcium  light ;  so  that  even  the  darkest  part  of  a  sun  spot 
outshines  the  lime  light.  The  brightest  part  of  an  electric  arc- 
light  comes  nearer  sunlight  in  intensity  than  anything  else  we 
know  of,  being  from  a  half  to  a  quarter  as  bright  as  the  solar 
surface  itself. 

The  sun's  disc  is  brightest  near  the  centre,  but  the  variation 
is  slight  until  we  get  pretty  near  the  edge,  where  the  light 
falls  off  rapidly.  Just  at  the  sun's  limb,  the  brightness  is  not 
much  more  than  a  third  as  great  as  at  the  centre.  The  color 
is  there  modified  also,  becoming  a  sort  of  an  orange-red.  This 
darkening  and  change  of  color  are  due  to  the  general  absorp- 
tion of  light  by  the  lower  portions  of  the  sun's  atmosphere. 
According  to  Langley,  if  this  atmosphere  were  suddenly  re- 
moved the  surface  would  shine  out  somewhere  from  two  to 
five  times  as  brightly  as  now,  and  its  tint  would  become 
strongly  blue,  like  the  color  of  an  electric  arc. 

187.   The  Quantity  of  Solar  Heat ;  the  Solar  Constant.  —  The 

"  solar  constant "  is  the  number  of  heat  units  which  a  square 
unit  of  the  earth's  surface,  unprotected  by  any  atmosphere  and 
squarely  exposed  to  the  sun's  rays,  would  receive  from  the  sun 
in  a  unit  of  time.  The  heat-unit  most  used  at  present  is  the 
"  calory,"  which  is  the  quantity  of  heat  required  to  raise  the 

1  The  standard  candle  is  a  sperm  candle  weighing  one- sixth  of  a  pound 
and  burning  120  grains  an  hour.  An  ordinary  gas-burner  usually  gives  a 
light  equivalent  to  from  ten  to  fifteen  candles. 


§  187]  THE   SUN'S    HEAT.  137 

temperature  of  one  kilogram  of  water  1°  C.  j  and  as  the  result 
of  the  best  observations  thus  far  made,  it  appears  that  the 
'  Solar  Constant7  is  between  twenty-five  and  thirty  of  these 
calories  to  a  square  metre  in  a  minute.  At  the  earth's  surface 
a  square  metre,  owing  to  the  absorption  of  a  large  percentage 
of  heat  by  the  air,  would,  however,  seldom  actually  receive 
more  than  from  ten  to  fifteen  calories  in  a  minute. 

The  method  of  determining  the  solar  constant  is  simple,  as 
far  as  the  principle  goes,  but  the  practical  difficulties  are 
serious,  and  thus  far  have  prevented  our  obtaining  all  the 
accuracy  desirable.  The  determination  is  made  by  allowing  a 
beam  of  sunlight  of  known  diameter  to  fall  upon  a  known 
quantity  of  water  for  a  known  time,  and  measuring  how  much 
the  water  rises  in  temperature.  The  principal  difficulty  lies 
in  determining  the  proper  allowance  to  be  made  for  absorption 
of  the  sun's  heat  in  passing  through  the  air.  Besides  this  it 
is  necessary  to  measure,  and  allow  for,  the  heat  which  is  re- 
ceived by  the  water  during  the  experiment  from  other  sources 
than  the  sun. 

188.  Solar  Heat  at  the  Earth's  Surface.  —  Since  it  requires 
about  eighty  calories  of  heat  to  melt  one  kilogram  of  ice,  it 
follows  that,  taking  the  solar  constant  at  twenty-five,  the  heat 
received  from  the  sun  when  overhead  would  melt  in  an  hour  a 
sheet  of  ice  about  three-quarters  of  an  inch  thick.  From  this 
it  is  easily  computed  that  the  amount  of  heat  received  by  the 
earth  from  the  sun  in  a  year  would  melt  a  shell  of  ice  137  feet 
thick  all  over  the  earth's  surface. 

If  we  accept  the  larger  value  of  the  solar  constant,  assigned  by 
Langley  (thirty  instead  of  twenty-five),  this  would  be  165  feet. 

Solar  heat  can,  of  course,  be  used  as  power,  and  so-called 
"solar  engines"  have  been  constructed  within  the  last  few 
years,  in  which  the  heat  received  upon  a  large  reflector  is 
made  to  evaporate  water  in  a  suitable  boiler  and  to  drive  a 


138  RADIATION  FROM  THE  SUN'S   SURFACE.  [§  188 

steam  engine.  It  is  found  that  the  heat  received  upon  a  re- 
flector ten  feet  square  can  be  made  to  give  practically  about 
one  horse-power. 

189.  Radiation  from  the  Sun's  Surface.  —  If  we  attempt  to 
estimate  the  intensity  of  the  radiation  from  the  surface  of  the 
sun  itself,  we  reach  results  which  are  simply  amazing.     We 
must  multiply  the  solar  constant  observed  at  the  earth  by  the 
square  of  the  ratio  between  the  earth's  distance  from  the  sun 
and  the  distance  of  the  sun's  surface  from  its  own  centre ;  i.e., 

by  the  square  of  f93'OOOOQO\  or  about  46,000 :  in  other  words, 
y   43,250    J 

the  amount  of  heat  emitted  in  a  minute  by  a  square  foot  of 
the  sun's  surface  is  about  46,000  times  as  great  as  that  received 
by  a  square  foot  of  surface  at  the  distance  of  the  earth.  Car- 
rying out  the  figures,  we  find  that  if  the  sun  were  frozen 
over  completely  to  a  depth  of  over  fifty  feet,  the  heat  it  emits 
would  be  sufncient  to  melt  the  ice  in  one  minute ;  that  if  a 
bridge  of  ice  could  be  formed  from  the  earth  to  the  sun  by  an 
ice-column  2^  miles  square,  and  if  in  some  way  the  entire  solar 
radiation  could  be  concentrated  upon  it,  it  would  be  melted  in 
one  second,  and  in  seven  more  would  be  dissipated  in  vapor. 

Expressing  it  in  terms  of  energy,  we  find  that  the  solar  radi- 
ation is  more  than  100,000  horse-power  continuously,  for  each 
square  metre  of  the  sun's  surface. 

So  far  as  we  can  now  see,  only  a  very  small  fraction  of  this  whole 
radiation  ever  reaches  a  resting-place.  The  earth  intercepts  about 
??oo  ooooTrg-  and  the  other  planets  of  the  solar  system  receive  in  all 
perhaps  from  ten  to  twenty  times  as  much.  Something  like  Tinnnnmnr 
seems  to  be  utilized  within  the  limits  of  the  solar  system. 

190.  The  Sun's  Temperature.  —  We  can  determine  with  some 
accuracy  the  amount  of  heat  which  the  sun  gives ;  to  find  its 
temperature  is  a  very  different  thing,  and  we  really  have  very 
little  knowledge  about  it,  except  that  it  must  be  extremely 


§  190]  CONSTANCY   OF   THE   SUN'S   HEAT.  139 

high,  —  far  higher  than  that  of  any  terrestrial  source  of  heat 
now  known.  The  difficulty  is  that  our  laboratory  experiments 
do  not  give  the  necessary  data  from  which  we  can  determine 
what  temperature  substances  like  those  of  which  the  sun  is 
composed  must  have,  in  order  to  enable  them  to  send  out 
heat  at  the  rate  which  we  observe.  Of  two  bodies  at  precisely 
the  same  temperature,  one  may  send  out  heat  a  hundred  times 
more  rapidly  than  the  other. 

The  estimates  as  to  the  temperature  of  the  photosphere  run 
all  the  way  from  the  very  low  ones  of  some  of  the  French 
physicists  (who  set  it  at  about  2500°  C.)  to  those  of  Secchi 
and  Ericsson,  who  put  the  figure  among  the  millions.  The 
prevailing  opinion  sets  it  between  5000°  and  10,000°  C.,  or 
from  9000°  to  18,000°  F. 

A  very  impressive  demonstration  of  the  intensity  of  the 
sun's  heat  is  found  in  the  fact  that  in  the  focus  of  a  powerful 
burning  lens  all  known  substances  melt  and  vaporize  ;  and  yet 
it  can  be  shown  that  at  the  focus  of  the  lens  the  temperature 
can  never  even  nearly  equal  that  of  the  source  from  which  the 
heat  is  derived. 

191.  Constancy  of  the  Sun's  Heat.  —  It  is  still  a  question 
whether  the  total  amount  of  the  sun's  radiation  does  or  does 
not  vary  from  time  to  time.  There  may  be  considerable  fluc- 
tuations in  the  hourly  or  daily  quantity  of  heat,  without  our 
being  able  to  detect  them  with  our  present  means  of  obser- 
vation. 

As  to  any  steady  progressive  increase  or  decrease  in  the 
amount  of  heat  received  from  the  sun,  it  is  quite  certain  that 
no  considerable  change  has  occurred  for  the  past  2000  years, 
because  the  distribution  of  plants  and  animals  on  the  earth's 
surface  is  practically  the  same  as  in  the  earliest  days  of  his- 
tory. It  is,  however,  rather  probable  than  otherwise  that  the 
great  changes  of  climate,  which  Geology  indicates  as  having 
formerly  taken  place  on  the  earth,  may  ultimately  be  traced 
to  changes  in  the  condition  of  the  sun. 


140  MAINTENANCE   OF    THE   SOLAR   HEAT.  [§  192 

192.  Maintenance  of  the  Solar  Heat.  —  We  cannot  here  dis- 
cuss the  subject  fully,  but  must  content  ourselves  with  saying, 
first,  negatively,  that   this   maintenance   cannot  be  accounted 
for  on  the  supposition  that  the  sun  is  a  hot  body,  solid  or 
liquid,  simply  cooling ;   nor  by  combustion  j   nor  (adequately) 
by  the  fall  of  meteors  on  the  sun's  surface,  though  this  cause 
undoubtedly  operates  to  a  limited  extent.     Second,  we  can  say 
positively  that  the  solar  radiation  can  be  accounted  for  on  the 
hypothesis  first  proposed  by  Helmholtz,  that  the  sun  is  mainly 
gaseous,   and  shrinking  slowly  but  continuously.     While  we 
cannot  see  any  such  shrinkage,  because  it  is  too  slow,  it  is  a 
matter  of  demonstration  that  if  the  sun's  diameter  should  con- 
tract about  300  feet  a  year,  heat  enough  would  be  generated 
to   keep  up  its  radiation  without  any  lowering  of  its   tem- 
perature.    If  the  shrinkage  were  more  than  about  300  feet, 
the  sun  would  be  hotter  at  the  end  of  the  year  than  it  was  at 
the  beginning. 

We  can  only  say  that  while  no  other  theory  meets  the  con- 
ditions of  the  problem,-  this  appears  to  do  so  perfectly,  and 
therefore  has  probability  in  its  favor. 

193.  Age  and  Duration  of  the  Sun. —  Of  course  if   this 
theory  is  correct,  the  sun's  heat  must  ultimately  come  to  an 
end ;  and  looking  backward  it  must  have  had  a  beginning.     If 
the  sun  keeps  up  its  present  rate  of  radiation,  it  must,  on  this 
hypothesis,  shrink  to  about  half  its  diameter  in  some  5,000000 
years  at  the  longest.     It  will  then  be  eight  times  as  dense  as 
now,  and  can  hardly  continue  to  be  mainly  gaseous,  so  that 
the  temperature  must  begin  to  fall  quite  sensibly.     It  is  not, 
therefore,  likely,  in  the  opinion  of  Professor  Newcomb,  that 
the  sun  will  continue  to  give  heat  sufficient  to  support  the 
present    conditions    upon    the    earth    for    much    more    than 
10,000000  years,  if  so  long. 

On  the  other  hand,  it  is  certain  that  the  shrinkage  of  the 
sun  to  its  present  dimensions  from  a  diameter  larger  than  that 


§  193]  CONSTITUTION   OF  THE   SUN.  141 

of  the  orbit  of  Neptune,  the  remotest  of  the  planets,  would 
produce  about  18,000000  times  as  much  heat  as  the  sun  now 
throws  out  in  a  year ;  hence,  IF  the  sun's  heat  has  been,  and 
still  is,  wholly  due  to  the  contraction  of  its  mass,  it  cannot  have 
been  emitting  heat  at  the  present  rate,  on  this  shrinkage  hy- 
pothesis, for  more  than  18,000000  years.  But  notice  the  'if.' 
It  is  quite  possible  that  the  solar  system  may  have  received 
in  the  past  supplies  of  heat  other  than  that  due  to  the  con- 
traction of  the  sun's  mass.  If  so,  it  may  be  much  older. 

194.  Constitution  of  the  Sun.  —  To  sum  up :  The  received 
opinion  as  to  the  constitution  of  the  sun  is  that  the  central 
mass,  or  nucleus,  is  probably  gaseous,  under  enormous  pressure, 
and  at  an  enormous  temperature. 

The  photosphere  is  probably  a  sheet  of  luminous  clouds,  con- 
stituted mechanically  like  terrestrial  clouds;  that  is,  of  small, 
solid,  or  liquid  particles  floating  in  gas. 

These  photospheric  clouds  float  in  an  atmosphere  composed 
of  those  gases  which  do  not  condense  into  solid  or  liquid  par- 
ticles at  the  temperature  of  the  solar  surface.  This  atmos- 
phere is  laden,  of  course,  with  the  vapors  out  of  which  the 
clouds  have  been  condensed,  and  constitutes  the  reversing  layer 
which  produces  the  dark  lines  of  the  solar  spectrum. 

The  chromosphere  and  prominences  appear  to  be  composed  of 
permanent  gases,  mainly  hydrogen  and  helium,  which  are  min- 
gled with  the  vapors  in  the  region  of  the  photosphere,  but  rise 
to  far  greater  elevations.  For  the  most  part  the  prominences 
appear  to  be  formed  by  jets  of  hydrogen,  ascending  through 
the  interstices  between  the  photospheric  clouds,  like  flames 
playing  over  a  coal  fire. 

As  to  the  corona,  it  is  as  yet  impossible  to  give  any  satis- 
factory explanation  of  all  the  phenomena  that  it  presents,  and 
since  thus  far  it  has  been  possible  to  observe  it  only  during 
the  brief  moments  of  total  eclipses,  progress  in  its  study  has 
been  necessarily  slow. 


142  ECLIPSES.  [  §  195 


CHAPTER  VII. 

ECLIPSES  AND  THE  TIDES. — FORM  AND  DIMENSIONS  OF 
SHADOWS.  —  ECLIPSES  OF  THE  MOON.  —  SOLAR  ECLIPSES, 
—  TOTAL,  ANNULAR,  AND  PARTIAL.  —  NUMBER  OF 
ECLIPSES  IN  A  YEAR. — RECURRENCE  OF  ECLIPSES 
AND  THE  SAROS.  —  OCCULTATIONS. — THE  TIDES. 

195.  The  word  Eclipse  (literally  a  ' swoon7)  is  a  term  ap- 
plied to  the  sudden  darkening  of  a  heavenly  body,  especially 
of  the  sun  or  moon.     An  eclipse  of  the  moon  is  caused  by  its 
passing  through  the  shadow  of  the  earth;  an  eclipse  of  the 
sun  by  the  moon's  passing  between  the  sun  and  the  observer, 
or,  what  comes  to  the  same  thing,  by  the  passage  of  the 
moon's  shadow  over  the  observer.     The  l  Shadow/  in  Astron- 
omy, is  the  space  from  which  sunlight  is  excluded  by  an  inter- 
vening body ;  speaking  geometrically,  it  is  a  solid,  not  a  surface. 
If  we  regard  the  sun  and  the  other  heavenly  bodies  as  spheri- 
cal, which,  of  course,  they  are  very  nearly,  these  shadows  are 
cones  with  their  axes  in  the  line  which  joins  the  centres  of  the 
sun  and   the   shadow-casting  body,  the   point   being   always 
directed  away  from  the  sun.     If  interplanetary  space  were  a 
little  hazy,  we  should  see  every  planet  accompanied  by  its 
shadow,  like  a  black  tail  behind  it. 

ECLIPSES  OF  THE  MOON. 

196.  Dimensions  of  the  Earth's   Shadow. — The  length  of 
the  shadow  is  easily  found.     In  Fig.  38,  0  is  the  centre  of  the 
sun  and  E  the  centre  of  the  earth,  and  aCb  is  the  shadow  of 


196] 


THE  EARTH  S   SHADOW. 


143 


the  earth  cast  by  the  sun.  It  is  readily  shown  by  Geometry 
that  if  we  call  EC,  the  length  of  the  shadow,  L,  and  OE,  the 
distance  of  the  earth  from  the  sun,  D,  then 

L  =  D  x  (    r    \  R  being  OA  the  radius  of  the  sun,  and  r 
v»  ~~  TJ 

the  radius  of  the  earth  Ea.     This  fraction,  (  _— - — \  is  about 

\R  -  rj 


L   :,  so  that  L  =  -r--U:  D. 


108.5'  108.5 

This  gives  857,000  miles  for  the  length  of   the  earth's 
shadow.    The  length  varies  about  14,000  miles  on  each  side 


FIG.  38.  — The  Earth's  Shadow. 

of  the  mean,  in  consequence  of  the  variation  of  the  earth's  dis- 
tance from  the  sun  at  different  times  of  the  year. 

From  the  cone  aCb  all  sunlight  is  excluded,  or  would  be  were  it  not 
for  the  fact  that  the  atmosphere  of  the  earth  bends  gome  of  the  rays 
which  pass  near  the  earth's  surface  into  its  shadow.  The  effect  of 
this  atmospheric  refraction  is  to  increase  the  diameter  of  the  shadow 
about  two  per  cent,  but  to  make  it  less  perfectly  dark. 

If  we  draw  the  lines,  Be  and  Ad,  crossing  at  P,  between  the 
earth  and  the  sun,  they  will  bound  the  penumbra,  within 
which  a  part,  but  not  the  whole,  of  the  sunlight  is  cut  off :  an 
observer  outside  of  the  shadow,  but  within  this  partly  shaded 
space,  would  see  the  earth  as  a  black  body  encroaching  on  the 
sun's  disc,  but  not  covering  it. 


144  LUNAR  ECLIPSES.  [§  197 

197.  Lunar    Eclipses.  —  The  axis,  or  central  line,  of  the 
earth's  shadow  is  always  directed  to  a  point  directly  opposite 
the  sun.     If,  then,  at  the  time  of  full  moon  the  moon  happens 
to  be  near  the  ecliptic,  i.e.,  not  far  from  one  of  the  nodes  (the 
points  where  her  orbit  cuts  the  ecliptic),  she  will  pass  through 
the  shadow  and  be  eclipsed.     Since,  however,  the  moon's  orbit 
is  inclined  5°  &'  to  the  ecliptic,  lunar  eclipses  do  not  happen 
very  frequently,  seldom  more  than  twice  a  year ;  because  the 
moon  at  the  full  usually  passes  north  or  south  of  the  shadow, 
without  touching  it. 

Lunar  eclipses  are  of  two  kinds,  partial  and  total;  total 
when  she  passes  completely  into  the  shadow;  partial  when 
she  only  partly  enters  it,  going  so  far  to  the  north  or  south  of 
the  centre  that  only  a  portion  of  the  disc  is  obscured.  An 
eclipse  of  the  moon  when  central  (i.e.,  when  the  moon  crosses 
the  centre  of  the  shadow)  may  continue  total  for  about  two 
hours,  the  interval  from  the  first  to  the  last  contact  being 
about  two  hours  more.  This  depends  upon  the  facts  that  the 
moon's  hourly  motion  is  nearly  equal  to  its  own  diameter,  and 
that  the  diameter  of  the  earth's  shadow  where  the  moon 
crosses  it  is  between  two  and  three  times  the  diameter  of  the 
moon  itself.  The  duration  of  an  eclipse  that  is  not  central  varies 
of  course  with  the  part  of  the  shadow  traversed  by  the  moon. 

198.  Phenomena  of  Total  Eclipses  of  the  Moon. — Half  an 
hour  or  so  before  the  moon  reaches  the  shadow,  its  edge  begins 
to  be  sensibly  darkened  by  the  penumbra,  and  the  edge  of  the 
shadow  itself,  when  it  first  touches  the  moon,  appears  nearly 
black  by  contrast  with  the  bright  parts  of  the  moon's  surface. 
To  the  naked  eye  the  outline  of  the  shadow  looks  fairly  sharp, 
but  even  with  a  small  telescope  it  appears  indefinite,  and  with 
a  large  telescope  of  high  magnifying  power  the  edge  of  the 
shadow  becomes  entirely  indistinguishable,  so  that  it  is  impos- 
sible to  determine  within  half  a  minute  or  so  the  time  when 
it  reaches  any  particular  point. 


§  198]  COMPUTATION   OF   A  LUNAR   ECLIPSE.  145 

After  the  moon  has  wholly  entered  the  shadow,  her  disc  is 
usually  distinctly  visible,  illuminated  with  a  dull  copper- 
colored  light,  which  is  sunlight  deflected  around  the  earth  into 
the  shadow  by  the  refraction  of  our  atmosphere,  as  illustrated 
by  Fig.  39.  The  brightness  of  the  moon's  disc  during  a  total 
eclipse  of  the  moon  differs  greatly  at  different  times,  according 

A 
A' 

FIG.  39.  —  Light  bent  into  Earth's  Shadow  by  Refraction. 

to  the  condition  of  the  weather  on  the  parts  of  the  earth  which 
happen  to  lie  at  the  edges  of  the  earth's  disc  as  seen  from  the 
moon.  If  it  is  cloudy  and  stormy  there,  little  light  will  reach 
the  moon ;  if  it  happens  to  be  clear,  the  quantity  of  light 
deflected  into  the  shadow  may  be  very  considerable.  In  the 
lunar  eclipse  of  1884,  the  moon  was  for  a  time  absolutely 
invisible  to  the  naked  eye,  a  very  unusual  circumstance. 

During  the  eclipse  of  Jan.  28th,  1888,  although  the  moon  was 
pretty  bright  to  the  eye,  Pickering  found  that  its  photographic  power, 
when  centrally  eclipsed,  was  only  about  rrrnnnnr  °f  what  it  had  been 
before  the  shadow  covered  it. 

199.  Computation  of  a  Lunar  Eclipse.  —  The  computation  of 
a  lunar  eclipse  is  not  at  all  complicated,  though  we  do  not  propose  to 
enter  into  it.  Since  all  its  phases  are  seen  everywhere  at  the  same 
absolute  instant  wherever  the  moon  is  above  the  horizon,  it  follows 
that  a  single  calculation  giving  the  Greenwich  times  of  the  different 
phenomena  is  all  that  is  needed.  Such  computations  are  made  and 
published  in  the  Nautical  Almanac.  The  observer  needs  only  to  cor- 
rect the  predicted  time  by  simply  adding  or  subtracting  his  longitude 
from  Greenwich,  in  order  to  get  the  true  local  time.  With  an  eclipse 
of  the  sun  the  case  is  very  different. 


146 


ECLIPSES   OF  THE  STJK. 


[§200 


ECLIPSES   OF  THE   SUN. 

200.  The  Length  of  the  Moon's  Shadow  is  very  nearly 
of  its  distance  from  the  sun,  and  averages  232,150  miles. 
It  varies  not  quite  4000  miles,  ranging  from  236,050  to 
238,300. 

Since  the  mean  length  of  the  shadow  is  less  than  the  mean 
distance  from  the  earth  (238,800  miles),  it  is  evident  that  on 
the  average  the  shadow  will  fall  short  of  the  earth.  The  eccen- 
tricity of  the  moon's  orbit,  however,  is  so  great  that  she  is 
sometimes  more  than  30,000  miles  nearer  than  at  others.  If 
when  the  moon  is  nearest  the  earth,  the  shadow  happens  to 
have  at  the  same  time  its  greatest  possible  length,  its  point 
may  reach  nearly  18,400  miles  beyond  the  earth's  surface.  In 


..» >  To  Sun 

FIG.  40.  —  The  Moon's  Shadow  on  the  Earth. 


M' 


this  CLse  the  "  cross-section  "  of  the  shadow,  where  the  earth's 
surface  cuts  it  (at  o  in  Fig.  40)  will  be  about  168  miles  in 
diameter,  which  is  the  largest  value  possible.  On  the  other 
hand,  when  the  moon  is  farthest  from  the  earth,  we  may  have 
the  state  of  things  indicated  by  placing  the  earth  at  B,  in  Fig. 
40.  The  vertex,  V,  of  the  shadow  will  then  fall  24,700  miles 
short  of  the  earth's  surface,  and  the  cross-section  of  the 
"shadow  produced"  will  have  a  diameter  of  206  miles  at  or, 
where  the  earth's  surface  cuts  it. 

201 .  Total  and  Annular  Eclipses.  —  To  an  observer  within 
the  shadow-cone  (i.e.,  between  V  and  the  moon,  Fig.  40),  the 
sun  will  be  totally  eclipsed.  An  observer  in  the  "  produced  " 
cone,  beyond  V,  will  see  the  moon  apparently  smaller  than  the 


§201]  PARTIAL  ECLIPSES.  147 

sun,  leaving  a  ring  of  the  sun  uneclipsed  ;  this  is  what  is 
called  an  "annular"  eclipse.  These  annular  eclipses  are  con- 
siderably more  frequent  than  the  total,  and  now  and  then  an 
eclipse  is  annular  in  part  of  its  course  across  the  earth,  and 
total  in  part.  This  is  when  the  point  of  the  moon's  shadow 
extends  beyond  the  surface  of  the  earth,  but  does  not  reach  as 
far  as  its  centre. 

The  track  of  the  eclipse  across  the  earth  will  of  course  be  a 
narrow  stripe  having  its  width  equal  to  the  cross-section  of 
the  shadow,  and  extending  across  the  hemisphere  which  is 
turned  towards  the  moon  at  the  time,  though  not  necessarily 
passing  the  centre  of  that  hemisphere.  Its  course  is  always 
from  the  west  towards  the  east,  but  usually  with  considerable 
motion  toward  the  north  or  south. 

202.  The  Penumbra  and  Partial  Eclipses.  —  The  penumbra 
can  easily  be  shown  to  have  a  diameter  on  the  line  CD  (Fig. 
40)  a  little  more  than  twice  the  diameter  of  the  moon,  or  over 
4000  miles.     An  observer  situated  within  this  penumbra  has  a 
partial  eclipse.     If  he  is  near  to  the  cone  of  the  shadow,  the 
sun  will  be  mostly  covered  by  the  moon;  if  near  the  outer 
edge  of  the  penumbra,  the  moon  will  but  slightly  encroach  on 
the  sun's  disc.     While,  therefore,  a  total  or  annular  eclipse  is 
visible  as  such  only  by  observers  within  the  narrow  path  trav- 
ersed by  the  shadow-spot,  the  same  eclipse  will  be  visible  as  a 
partial  one  anywhere  within  2000  miles  on  each  side  of  the 
path ;  and  the  2000  miles  must  be  reckoned  square  to  the  axis 
of  the  shadow,  and  may  correspond  to  a  much  greater  distance 
when  reckoned  around  upon  the  spherical  surface  of  the  earth. 

203.  Velocity  of  the  Shadow,  and  Duration  of  an  Eclipse. 

—  Were  it  not  for  the  earth's  rotation,  the  moon's  shadow 
would  pass  the  observer  at  the  rate  of  about  2100  miles  an 
hour.  The  earth,  however,  is  rotating  towards  the  east  in  the 
same  general  direction  as  that  in  which  the  shadow  moves, 
so  that  the  relative  velocity  is  usually  much  less. 


148  PHENOMENA   OF   A   SOLAR   ECLIPSE.  [§  203 

A  total  eclipse  of  the  sun  observed  at  a  station  near  the 
equator,  under  the  most  favorable  conditions  possible,  may 
continue  total  for  7m  58".  In  latitude  40°  the  duration  can 
barely  equal  6J-m.  At  the  equator  an  annular  eclipse  may 
last  for  12m  24",  the  maximum  width  of  the  ring  of  the  sun 
visible  around  the  moon  being  1'  37". 

In  the  observation  of  an  eclipse,  four  contacts  are  recognized :  the 
first,  when  the  edge  of  the  moon  first  touches  the  edge  of  the  sun  ;  the 
second,  when  the  eclipse  becomes  total  or  annular ;  the  third,  at  the  ces- 
sation of  the  total  or  annular  phase ;  and  the  fourth,  when  the  moon 
finally  leaves  the  solar  disc.  From  the  first  contact  to  the  fourth  the 
time  may  be  a  little  over  two  hours.  In  a  partial  eclipse,  only  the 
first  and  fourth  are  observable,  and  the  interval  between  them  may  be 
very  small  when  the  moon  just  grazes  the  edge  of  the  sun. 

The  magnitude  of  an  eclipse  is  usually  reckoned  in  "  digits,"  the 
digit  being  T*y  of  the  sun's  diameter.  An  eclipse  of  nine  digits  is 
one  in  which  the  disc  of  the  moon  covers  three-fourths  of  the  sun's 
diameter  at  the  middle  of  the  eclipse. 

204.  Phenomena  of  a  Solar  Eclipse.  —  There  is  nothing  of 
special  interest  until  the  sun  is  mostly  covered,  though  before 
that  time  the  shadows  cast  by  the  foliage  begin  to  be  peculiar. 

The  light  shining  through  every  small  interstice  among  the  leaves, 
instead  of  forming  as  usual  a  circle  on  the  ground,  makes  a  little  cres- 
cent—  an  image  of  the  partly  covered  sun. 

About  ten  minutes  before  totality  the  darkness  begins  to  be 
felt,  and  the  remaining  light,  coming  as  it  does  from  the  edge 
of  the  sun,  is  not  only  faint  but  yellowish,  more  like  that  of  a 
calcium  light  than  sunshine.  Animals  are  perplexed  and 
birds  go  to  roost.  The  temperature  falls,  and  dew  appears. 
In  a  few  moments,  if  the  observer  is  so  situated  that  his  view 
commands  the  distant  western  horizon,  the  moon's  shadow  is 
seen  coming,  much  like  a  heavy  thunder  shower,  and  advanc- 
ing with  almost  terrifying  swiftness.  As  soon  as  the  shadow 
arrives,  and  sometimes  a  little  before,  the  corona  and  promi- 


§  204]  CALCULATION  OF  A  SOLAR   ECLIPSE.  149 

nences  become  visible,  while  the  brighter  planets  and  stars  of 
the  first  three  magnitudes  make  their  appearance. 

The  suddenness  with  which  the  darkness  pounces  upon  the 
observer  is  startling.  The  sun  is  so  brilliant  that  even  the 
small  portion  which  remains  visible  up  to  the  moment  of 
total  obscuration  so  dazzles  the  eye  that  it  is  unprepared  for 
the  sudden  transition.  In  a  few  moments,  however,  the  eye 
adjusts  itself,  and  it  is  found  that  the  darkness  is  really  not 
very  intense.  If  the  totality  is  of  short  duration,  say  not 
more  than  two  minutes,  there  is  not  much  difficulty  in  reading 
an  ordinary  watch-face.  In  an  eclipse  of  long  duration  (four 
or  five  minutes)  it  is  much  darker,  and  lanterns  become 
necessary. 

205.  Calculation  of  a  Solar  Eclipse.  —  A  solar  eclipse  cannot 
be  dealt  with  in  any  such  summary  way  as  a  lunar  eclipse,  because 
the  times  of  contact  and  the  phenomena  are  different  at  every  differ- 
ent station.      The  path  which  the  shadow  of  a  total  eclipse  will 
describe  upon  the  earth  is  roughly  mapped  out  in  the  Nautical  Alma- 
nacs several  years  beforehand,  and  with  the  chart  are  published  the 
data  necessary  to  enable  one  to  calculate  with  accuracy  the  phenomena 
for  any  given  station ;  but  the  computation  is  rather  long  and  some- 
what complicated. 

Oppolzer,  a  Viennese  astronomer,  published  a  few  years  ago  a 
remarkable  book  entitled  "The  Canon  of  Eclipses,"  containing  the 
elements  of  all  eclipses  (8000  solar  and  5200  lunar)  occurring  between 
the  year  1207  B.C.  and  2162  A.D.,  with  maps  showing  the  approximate 
tracks  of  all  the  solar  eclipses. 

206.  Frequency  of  Eclipses  and  Number  in  a  Year.  —  The 

least  possible  number  in  a  year  is  two,  both  of  the  sun ;  the 
largest  seven,  five  solar  and  two  lunar :  the  most  usual  number 
is  four.  The  eclipses  of  a  given  year  always  take  place  at  two 
opposite  seasons,  which  may  be  called  the  "  eclipse  months  " 
of  the  year,  near  the  times  when  the  sun  crosses  the  nodes  of 
the  moon's  orbit.  Since  the  nodes  move  westward  around  the 
ecliptic  once  in  about  nineteen  years  (Art.  134),  the  time  oc- 


150  RECURRENCE   OF   ECLIPSES.  [§  206 

cupied  by  the  sun  in  passing  from  a  node  to  the  same  node 
again  is  only  346.62  days,  which  is  sometimes  called  the 
"  eclipse  year." 

Taking  the  whole  earth  into  account,  the  solar  eclipses  are 
the  more  numerous,  nearly  in  the  ratio  of  3:2.  It  is  not  so, 
however,  with  those  that  are  visible  at  a  given  place.  A  solar 
eclipse  can  be  seen  only  by  persons  who  happen  to  be  on  the 
track  described  by  the  moon's  shadow  in  its  passage  across 
the  globe,  while  a  lunar  eclipse  is  visible  over  considerably 
more  than  half  the  earth,  either  at  its  beginning  or  end, 
if  not  throughout  its  whole  duration,  —  and  this  more  than 
reverses  the  proportion;  i.e.,  at  any  given  place  lunar  eclipses 
are  considerably  more  frequent  than  solar.  Solar  eclipses  that 
are  total  somewhere  or  other  on  the  earth's  surface  are  not 
very  rare,  averaging  about  one  for  every  year  and  a  half.  But 
at  any  given  place  a  total  eclipse  happens  only  once  in  about 
360  years  in  the  long  run. 

During  the  19th  century,  six  shadow-tracks  have  already  traversed 
the  United  States,  and  one  more  will  do  so  on  May  27th,  1900,  the 
path  in  this  case  running  from  Texas  to  Virginia. 

207.  Recurrence  of  Eclipses ;  the  Saros.  —  It  was  known  to 
the  Egyptians,  even  in  prehistoric  times,  that  eclipses  occur 
at  regular  intervals  of  18  years  and  11-J-  days  (10^  days  if  there 
happen  to  be  five  leap  years  in  the  interval).  They  named 
this  period  the  "  Saros."  It  consists  of  223  synodic  months, 
containing  6585.32  days,  while  19  "eclipse  years"  contain 
6585.78.  The  difference  is  only  about  11  hours,  in  which  time 
the  sun  moves  on  the  ecliptic  about  28'.  If,  therefore,  a  solar 
eclipse  should  occur  to-day  with  the  sun  exactly  at  one  of  the 
moon's  nodes,  at  the  end  of  223  months  the  new  moon  will 
find  the  sun  again  close  to  the  node  (only  28'  west  of  it),  and 
a  very  similar  eclipse  will  occur  again ;  but  the  track  of  this 
new  eclipse  will  lie  about  8  hours  of  longitude  farther  west  on 
the  earth,  on  account  of  the  odd  .32  of  a  day  in  the  Saros. 


§207]  CAUSE  OF  THE  TIDES.  151 

The  usual  number  of  eclipses  in  a  Saros  is  a  little  over  70, 
varying  two  or  three  one  way  or  the  other. 

In  the  Saros  closing  Dec.  22d,  1889,  the  total  number  was  72, —  29 
lunar  and  43  solar.  Of  the  latter,  29  were  central  (13  total,  16  annu- 
lar), and  14  were  only  partial. 


THE  TIDES. 

208.  Cause  of  the  Tides.  —  Since  the  tides  depend  upon  the 
action  of  the  sun  and  of  the  moon  upon  the  waters  of  the 
earth,  they  may  properly  be  considered  here  before  we  deal 
with  the  planetary  system.  We  do  not  propose  to  go  into  the 
mathematical  theory  of  the 
phenomena  at  all,  as  it  lies 
far  beyond  our  limitations ; 
but  any  person  can  see  that 
a  liquid  globe  falling  freely 
towards  an  attracting  body, 
which  attracts  the  nearer  por- 
tions more  powerfully  than 

.__  .  J  ,  FIG.  41.  — The  Tides. 

the  more  remote,  will  be  drawn 

out  into  an  elongated  lemon-shaped  form,  as  illustrated  in 
Fig.  41 ;  and  if  the  globe,  instead  of  being  liquid,  is  mainly 
solid,  but  has  large  quantities  of  liquid  on  its  surface,  substan- 
tially the  same  result  will  follow.  Now  the  earth  is  free  in 
space,  and  though  it  has  other  motions,  it  is  also  falling  towards 
the  moon  and  towards  the  sun,  and  is  affected  precisely  as  it 
would  be  if  its  other  motions  did  not  exist.  The  consequence 
is  that  at  any  time  there  is  a  tendency  to  elongate  those  diam- 
eters of  the  earth  which  are  pointed  towards  the  moon  and 
towards  the  sun.  The  sun  is  so  much  farther  away  than  the 
moon  that  its  effect  in  thus  deforming  the  surface  of  the 
earth  is  only  about  two-fifths  as  great  as  that  of  the  moon. 


152  DEFINITIONS.  [§  209 

209.  The  tides  consist  in  a  regular  rise  and  fall  of  the  ocean 
surface,   the   average   interval    between    corresponding    high 
waters  on  successive  days  at  any  given  place  being  twenty- 
four  hours  and  fifty-one  minutes,  which  is  precisely  the  same 
as  the  average  interval  between  two  successive  passages  of  the 
moon  across  the  meridian ;  and  since  this  coincidence  is  main- 
tained indefinitely,  it  of  itself  makes  it  certain  that  there  must 
be  some  causal  connection  between  the  moon  and  the  tides. 
Some  one  has  said  that  the  odd  fifty-one  minutes  is  the  moon's 
"  ear  mark." 

That  the  moon  is  largely  responsible  for  the  tides  is  also 
shown  by  the  fact  that  when  the  moon  is  in  perigee,  at  the 
nearest  point  to  the  earth,  the  tides  are  nearly  twenty  per  cent 
higher  than  when  she  is  in  apogee. 

210,  Definitions.  —  While  the  water  is  rising,  it  is  flood  tide ; 
while  falling,  it  is  ebb  tide.     It  is  high  water  at  the  moment 
when  the  water  level  is  highest,  and  low  water  when  it  is 
lowest.     The  spring  tides  are  the  largest  tides  of  the  month, 
which  occur  near  the  times  of  new  and  full  moon,  while  the 
neap  tides  are  the  smallest,  and  occur  at  half  moon,  the  rela- 
tive heights  of  spring  and  neap  tides  being  about  as  7 : 3.     At 
the  time  of  the  spring  tides,  the  interval  between  the  corre- 
sponding tides  of  successive  days  is  less  than  the  average, 
being  only  about  24  hours,  38  minutes  (instead  of  24  hours, 
51  minutes),  and  then  the  tides  are  said  to  prime.    At  the  neap 
tides,  the  interval  is  greater  than  the  mean,  —  about  25  hours, 
6  minutes,  and  the  tide  lags.    The  establishment  of  a  port  is 
the  mean  interval  between  the  time  of  high  water  at  that  port 
and  the  next  preceding  passage  of  the  moon  across  the  merid- 
ian.    The  "establishment"  of  New  York,  for  instance,  is  8 
hours,  13  minutes.     The  actual  interval  between  the  moon's 
transit  and  high  water  varies,  however,  nearly  half  an  hour 
on  each  side  of  this  mean  value  at  different  times  of  the 
month,  and  under  varying  conditions  of  the  weather. 


§  211]  MOTION   OF   THE   TIDES.  153 

211.  Motion  of  the  Tides.  —  If  the  earth  were  wholly  com- 
posed of  water,  and  if  it  kept  always  the  same  face  towards  the 
moon,  as  the  moon  does  towards  the  earth,  then  (leaving  out 
of  account  the  sun's  action  for  the  present)  a  permanent  tide 
would  be  raised  upon  the  earth,  as  indicated  in  Fig.  41.  The 
difference  between  the  water  level  at  A  and  D  would  be  a 
little  less  than  two  feet.  Suppose,  now,  the  earth  put  in  rota- 
tion. It  is  easy  to  see  that  the  two  tidal  waves  A  and  B  would 
move  over  the  earth's  surface,  following  the  moon  at  a  certain 
angle  dependent  on  the  inertia  of  the  water,  and  tending  to 
move  with  a  westward  velocity  equal  to  the  earth's  eastward 
rotation,  —  about  a  thousand  miles  an  hour  at  the  equator. 
The  sun's  action  would  produce  similar  tides  superposed  upon 
the  moon's  tide,  and  about  two-fifths  as  large,  and  at  different 
times  of  the  month  these  two  pairs  of  tides  would  sometimes 
conspire  and  sometimes  be  opposed. 

If  the  earth  were  entirely  covered  with  deep  water,  the  tide 
waves  would  run  around  the  globe  regularly ;  and  if  the  depth 
of  the  water  were  not  less  than  thirteen  miles,  the  tide  crests, 
as  can  be  shown  (though  we  do  not  undertake  it  here),  would 
follow  the  moon  at  an  angle  of  just  90° :  it  would  be  high  water 
just  where  it  might  at  first  be  supposed  we  should  get  low 
water,  the  place  of  high  water  being  shifted  90°  by  the  rota- 
tion of  the  earth. 

If  the  depth  of  the  water  were,  as  it  really  is,  much  less 
than  thirteen  miles,  the  tide  wave  in  the  ocean  could  not  keep 
up  with  the  moon,  and  this  would  complicate  the  results. 
Moreover,  the  continents  of  North  and  South  America,  with 
the  southern  Antarctic  continent,  make  a  barrier  almost  from 
pole  to  pole,  leaving  only  a  narrow  passage  at  Cape  Horn.  As 
a  consequence  it  is  quite  impossible  to  determine  by  theory 
what  the  course  and  character  of  tide  waves  must  be.  We 
have  to  depend  upon  observations,  and  observations  are 
more  or  less  inadequate,  because,  with  the  exception  of  a 
few  islands,  our  only  possible  tide  stations  are  on  the  shores 


154  FREE  AND  FOECED  OSCILLATIONS.  [§  211 

of  continents  where  local  circumstances  largely  control  the 
phenomena. 

212.  Free  and  Forced  Oscillations. — If  the  water  of  the 
ocean  is  suddenly  disturbed,  as,  for  instance,  by  an  earth- 
quake, and  then  left  to  itself,  a  "  free  wave  "  is  formed,  which, 
if  the  horizontal  dimensions  of  the  wave  are  large  as  compared 
with  the  depth  of  the  water  (i.e.,  if  it  is  many  hundred  miles 
in  length),  will  travel  at  a  rate  which  depends  simply  on  the 
depth  of  the  water. 

Its  velocity  is  equal,  as  can  be  proved,  to  the  velocity  acquired  by  a 
body  in  falling  through  half  the  depth  of  the  ocean.  Observations 
upon  waves  caused  by  certain  earthquakes  in  South  America  and 
Japan  have  thus  informed  us  that  between  the  coasts  of  those  coun- 
tries the  Pacific  averages  between  two  and  one-half  and  three  miles  in 
depth. 

Now  as  the  moon  in  its  apparent  diurnal  motion  passes 
across  the  American  continent  each  day  and  comes  over  the 
Pacific  Ocean,  it  starts  such  a  "parent"  wave  in  the  Pacific, 
and  a  second  one  is  produced  twelve  hours  later.  These  waves, 
once  started,  move  on  nearly  (but  not  exactly)  like  a  free  earth- 
quake wave :  not  exactly,  because  the  velocity  of  the  earth's 
rotation  being  about  1040  miles  at  the  equator,  the  moon 
moves  (relatively)  westward  faster  than  the  wave  can  natu- 
rally follow  it ;  and  so  for  a  while  the  moon  slightly  acceler- 
ates the  wave.  The  tidal  wave  is  thus,  in  its  origin,  a  "  forced 
oscillation "  :  in  its  subsequent  travel  it  is  very  nearly,  but 
not  entirely,  "  free." 

Of  course  as  the  moon  passes  on  over  the  Indian  and  Atlan- 
tic oceans,  it  starts  waves  in  them  also,  which  combine  with 
the  parent  wave  coming  in  from  the  Pacific. 

213.  Course  of  Travel  of  the  Tide  Wave.  —  The  parent  wave 
appears  to  start  twice  a  day  in  the  Pacific  Ocean,  off  Callao,  on  the 


§  213]  HEIGHT  OF  THE  TIDES.  155 

coast  of  South  America.  From  this  point  the  wave  travels  northwest 
through  the  deep  water  of  the  Pacific,  at  the  rate  of  about  850  miles  an 
hour,  reaching  Kamtchatka  in  ten  hours.  Through  the  shallow  water 
to  the  west  and  southwest  the  velocity  is  only  from  400  to  600  miles  an 
hour,  so  that  the  wave  is  six  hours  old  when  it  reaches  New  Zealand. 
Passing  on  by  Australia  and  combining  with  the  small  wave  which  the 
moon  starts  in  the  Indian  Ocean,  the  resultant  tide  crest  reaches  the 
Cape  of  Good  Hope  in  about  twenty-nine  hours,  and  enters  the 
Atlantic.  Here  it  combines  with  a  smaller  tide  wave,  twelve  hours 
younger,  which  has  "  backed "  into  the  Atlantic  around  Cape  Horn, 
and  it  is  also  modified  by  the  direct  tide  produced  by  the  moon's 
action  upon  the  Atlantic.  The  tide  resulting  from  the  combination  of 
these  three  then  travels  northward  through  the  Atlantic  at  the  rate  of 
about  700  miles  an  hour.  It  is  about  forty  hours  old  when  it  first 
reaches  the  coast  of  the  United  States  in  Florida ;  and  our  coast  lies 
in  such  a  direction  that  it  arrives  at  all  the  principal  ports  within  two 
or  three  hours  of  the  same  time.  It  is  forty-one  or  forty-two  hours 
old  when  it  reaches  New  York  and  Boston.  To  reach  London,  it  has 
to  travel  around  the  northern  end  of  Scotland  and  through  the  North 
Sea,  and  is  nearly  sixty  hours  old  when  it  arrives  at  that  port. 

In  the  great  oceans  there  are  three  or  four  such  tide  crests,  follow- 
ing nearly  in  the  same  track,  but  with  continual  minor  changes. 

214.  Height  of  the  Tides. —In  mid-ocean  the  difference 
between  high  and  low  water  is  usually  between  two  and  three 
feet,  as  observed  on  isolated  islands  in  the  deep  water.  On 
the  continental  shores  the  height  is  ordinarily  much  greater. 

j^  ^_c^        ^     ^    A    r 

^  ^^  ^ ^  ^^  v  v  v 

PIG.  42.  —  Increase  in  Height  of  Tide  on  approaching  the  Shore. 

As  soon  as  the  tide  wave  "touches  bottom/7  so  to  speak,  the 
velocity*  is  diminished,  the  tide  crests  are  crowded  more  closely 
together,  and  the  height  of  the  tide  is  very  much  increased,  as 
indicated  in  Fig.  42. 


156  TIDES   IN   RIVEKS.  [§  214 

Theoretically  it  varies  inversely  as  the  fourth  root  of  the  depth  ;  i.e., 
where  the  water  is  100  feet  deep,  the  tide  wave  should  be  twice  as 
high  as  at  the  depth  of  1600  feet. 

Where  the  configuration  of  the  shore  forces  the  tide  into  a 
corner,  it  sometimes  rises  very  high.  At  Annapolis  on  the 
Bay  of  Fundy,  tides  of  seventy  feet  are  not  uncommon,  and  an 
altitude  of  100  feet  is  said  to  occur  sometimes.  At  Bristol 
in  the  English  Channel,  tides  of  forty  or  fifty  feet  are  reached ; 
at  the  same  time  on  the  coast  of  Ireland,  just  opposite,  the 
tide  is  very  small. 

215.  Tides  in  Rivers.  —  The  tide  wave  ascends  a  river  at  a  rate 
which  depends  upon  the  depth  of  the  water,  the  amount  of  friction, 
and  the  swiftness  of  the  stream.  It  may,  and  generally  does,  ascend 
until  it  cornes  to  a  rapid  where  the  velocity  of  the  current  is  greater 
than  that  of  the  wave.  In  shallow  streams,  however,  it  dies  out 
earlier.  Contrary  to  what  is  usually  supposed,  it  often  ascends  to  an 
elevation  far  above  that  of  the  highest  crest  of  the  tide  wave  at  the 
river's  mouth.  In  the  La  Plata  and  Amazon,  the  tide  goes  up  to  an 
elevation  of  at  least  100  feet  above  the  sea-level.  The  velocity  of  a 
tide  wave  in  a  river  seldom  exceeds  ten  or  twenty  miles  an  hour,  and 
is  ordinarily  much  less. 


§  216]  THE  PLANETS   IN   GENERAL.  157 


CHAPTER  VIII. 

THE  PLANETAEY   SYSTEM. 

THE  PLANETS  IN  GENERAL.  —  THEIR  NUMBER,  CLASSI- 
FICATION, AND  ARRANGEMENT.  —  BODE'S  LAW.  —  THEIR 
ORBITS.  —  KEPLER'S  LAWS  AND  GRAVITATION.  —  AP- 
PARENT MOTIONS  AND  THE  SYSTEMS  OF  PTOLEMY 
AND  COPERNICUS. — DETERMINATION  OF  DATA  RELAT- 
ING TO  THE  PLANETS,  THEIR  DIAMETER,  MASS,  ETC.  — 

HERSCHEL'S  ILLUSTRATION  OF  THE  SOLAR  SYSTEM. — 

DESCRIPTION  OF  THE  TERRESTRIAL  PLANETS,  MERCURY, 
VENUS,   AND   MARS. 

216.  THE  earth  is  one  of  a  number  of  bodies  called  planets 
which  revolve  around  the  sun  in  oval  orbits  that  are  nearly 
circular  and  lie  nearly  in  one  plane  or  level.     There  are  eight 
of  them  which  are  of  considerable  size,  besides  a  group  of  sev- 
eral hundred  minute  bodies  called  the  asteroids,  which  seem 
to   represent  in  some  way  a  ninth  planet,  either  broken  to 
pieces  or  somehow  ruined  in  the  making. 

217.  Classification  of  the  Planets. — The  four  inner  ones 
have  been  called  by  Humboldt  the  terrestrial  planets,  because 
the  earth  is  one  of  them,  and  the  others  resemble  it  in  size 
and  density.     In  the  order  of  distance  from  the  sun  they  are 
Mercury,  Venus,  the  earth,  and  Mars.      The  four  outer  ones 
Humboldt  calls  the  major  planets,  because   they  are  much 
larger  and  move  in  larger  orbits.     They  seem  to  be  bodies  of 
a  different  sort  from  the  earth,  very  much  less   dense   and 


158 


BODE'S  LAW. 


[§217 


probably  of  higher  temperature.  They  are  Jupiter,  Saturn, 
Uranus,  and  Neptune.  The  asteroids  (from  the  Greek  aster- 
eidos,  i.e.,  star-like  planets),  called  by  some  planetoids,  or 
minor  planets,  all  lie  in  the  vacant  space  between  Mars  and 
Jupiter,  and  appear  to  contain  in  the  aggregate  about  as  much 
material  as  would  make  a  planet  not  far  from  the  size  of  Mars. 
All  of  the  planets  except  Mercury  and  Venus  have  satellites. 
The  earth  has  one,  Mars  two,  Jupiter  four,  Saturn  eight, 
Uranus  four,  Neptune  one,  —  twenty  in  all. 

218.   The  following  little  table  contains  in  round  numbers 
the  principal  numerical  facts  as  to  the  planets :  — 


NAME. 

DISTANCE  IN 
ASTRONOMICAL 
UNITS. 

PERIOD. 

DIAMETER. 

Mercury 

04 

3  months 

3000  miles 

Venus  

07 

7^  months 

7700     " 

Earth  . 

10 

1  year 

7918    " 

Mars 

1  5 

1  yr  10  mos 

4200     " 

Asteroids  

3.0  ± 

3  years  to  9  years 

200  to  10  miles 

Jupiter  

52 

11  9  years 

86,000  miles 

Saturn  

95 

295      " 

73  000     " 

Uranus 

192 

8^0      " 

32  000     " 

Neptune 

301 

1648      " 

35  000     " 

This  table  should  be  learned  by  heart.  More  accurate  data 
will  be  given  hereafter,  but  the  round  numbers  are  quite  suf- 
ficient for  all  ordinary  purposes,  and  are  much  more  easily 
remembered. 

219.  Bode's  Law.  —  If  we  set  down  a  row  of  4's,  to  the 
second  4  add  3,  to  the  third  6,  to  the  fourth  12,  etc.,  a  series  of 
numbers  will  result  which,  divided  by  10,  will  represent  the 
planetary  distances  very  nearly,  except  in  the  case  of  Neptune, 


§219]  KEPLER'S  LAWS.  159 

whose  distance  is  only  30  instead  of  38,  as  the  rule  would 
make  it.     Thus  — 

444444  4  4  4 

3          6        12        24        48          96        192        384 

4        7        10        16       [28]       52         100        196        388 

$      2       0       £       ®       :y        b         ¥         v 

(The  characters  below  the  numbers  are  the  symbols  of  the 
planets,  used  in  almanacs  instead  of  their  names.) 

This  law  seems  to  have  been  first  noticed  by  Titius  of  Wittenberg, 
but  bears  the  name  of  Bode,  Director  of  the  Observatory  of  Berlin, 
who  first  secured  general  attention  to  it. 

No  logical  reason  can  yet  be  given  for  it.  It  may  be  a  mere  con- 
venient coincidence,  or  it  may  be  the  result  of  the  process  of  develop- 
ment which  brought  the  solar  system  into  its  present  state. 

220.  Kepler's  Laws.  —  Three  famous  laws  discovered  by 
Kepler  (1607-1620)  govern  the  motions  of  the  planets :  — 

I.  The  orbit  of  each  planet  is  an  ellipse  with  the  sun  in  one 
of  its  foci.     (See  Appendix,  Art.  429,  for  a  description  of  the 
ellipse.) 

II.  In  the  motion  of  each  planet  around  the  sun,  the  radius 
vector  describes  equal  areas  in  equal  times.     (See  Art.  121, 
Fig.  13,  for  illustration.) 

III.  The  squares  of  the  periods  of  the  planets  are  propor- 
tional to  the  cubes  of  their  mean  distances  from  the  sun.    This 
is  known  as  the  Harmonic  Law.     Stated  as  a  proportion  it 
reads  :  P-f :  P22 : :  A-f :  A2S,  or  in  words  :  The  square  of  the  period 
of  planet  No.  1 :  square  of  the  period  of  planet  No.  2 : :  cube  of 
the  mean  distance  of  planet  No.  1 :  cube  of  the  mean  distance  of 
planet  No.  2.    Planets  No.  1  and  No.  2  are  any  pair  of  planets 
selected  at  pleasure.     (For  fuller  illustration,  see  Appendix, 
Art.  430.) 

It  was  the  discovery  of  this  law  which  so  filled  Kepler  with 
enthusiasm  that  he  wrote,  "  If  God  has  waited  6000  years  for 
a  discoverer,  I  can  wait  as  long  for  a  reader." 


160  GRAVITATION.  [§  221 

221.  Gravitation.  —  When   Kepler    discovered   these   three 
laws  he  could  give  no  reason  for  them  —  no  more  than  we 
can  now  for  Bode's  law ;  —  but  some  sixty  years  later  Newton 
discovered  that  they  all  follow  necessarily  as  the  consequence 
of  the  law  of  gravitation,  which  he  had  discovered ;   namely, 
that   "every  particle  of  matter  in  the   universe   attracts  every 
other  particle  with  a  force  that  varies  directly  as  the  masses  of  the 
particles,  and  inversely  as  the  square  of  the  distance  between 
them"     It  would  take  us  far  beyond  our  limits  to  attempt  to 
show  how  Kepler's  laws  follow  from  this,  but  they  do.     The 
only  mystery  in  the  case  is  the  mystery  of  the  "  attraction " 
itself;   for  this  word  "attraction'7  is  to  be  taken  as  simply 
describing  an  effect  without  in  the  least  explaining  it. 

Things  take  place  as  if  the  atoms  had  in  themselves  intelligence  to 
recognize  each  other's  positions,  and  power  to  join  hands  in  some  way, 
and  pull  upon  each  other  through  the  intervening  space,  whether  it 
be  great  or  small.  But  neither  Newton  nor  any  one  else  supposes  that 
atoms  are  really  endowed  with  any  such  power,  and  the  explanation 
of  gravity  remains  to  be  found :  very  probably  it  is  somehow  involved 
in  that  constitution  of  the  material  universe  which  makes  possible  the 
transmission  through  space  of  light  and  heat,  and  electric  and  mag- 
netic forces. 

222.  Sufficiency  of    Gravitation  to  explain  the  Planetary 
Motions.  —  We  wish  to  impress  as  distinctly  as  possible  upon 
the  student  one  idea;  this  namely,  that  given  a  planet  once  in 
motion,  nothing  further  than  gravitation  is  required  to  explain 
perfectly  all  its  motions   forever  after.     Many  half-educated 
people  have  an  idea  that  some  other  force  or  mechanism  must 
act  to  keep  the  planets  going.     This  is  not  so :  not  a  single 
motion  in  the  whole  planetary  system  has  ever  yet  been  de- 
tected for  which  gravitation  fails  to  account. 

223.  Map  of  the  Orbits.  —  Fig.  43  shows  the  smaller  orbits 
of  the  system  (including  the  orbit  of  Jupiter)  drawn  to  scale, 


223] 


SMALLER    PLANETARY   ORBITS. 


161 


the  radius  of  the  earth's  orbit  being  taken  as  four-tenths  of  an 
inch. 

On  this  scale,  the  diameter  of  Saturn's  orbit  would  be  7.4  inches, 
that  oi'  Uranus  would  be  13.4:  inches,  and  that  of  Neptune  about  two 


FIG.  43.  —  Plan  of  the  Smaller  Planetary  Orbits. 

feet.     The  nearest  fixed  star,  on  the  same  scale,  would  be  a  mile  and 
a  quarter  away. 

It  will  be  seen  that  the  orbits  of  Mercury,  Mars,  Jupiter, 
and  several  of  the  asteroids  are  quite  distinctly  "  out  of  cen- 


162  INCLINATION  OF  THE  ORBITS.  [§  223 

tre "  with  respect  to  the  sun.  The  orbits  are  so  nearly  cir- 
cular that  there  is  no  noticeable  difference  between  their 
length  and  their  breadth,  but  the  eccentricity  shows  plainly 
in  the  position  of  the  sun. 

224.  Inclination  of  the  Orbits.  —  The  orbits  are  drawn  as  if 
they  all  lay  on  the  plane  of  the  ecliptic ;  i.e.,  on  the  surface  of 
the  paper.    This  is  not  quite  correct.    The  orbit  of  the  asteroid 
Pallas  should  be  really  tipped  up  at  an  angle  of  nearly  30°, 
and  that  of  Mercury,  which  is  more  inclined  to  the  ecliptic 
than  the  orbit  of  any  other  of  the  principal  planets,  is  sloped 
at  an  angle  of  7°.     The   inclinations,  however,  are  so  small 

(excepting  the  asteroids) 
that  they  may  be  neg- 
lected for  ordinary  pur- 
poses. On  the  scale  of 
the  diagram,  Neptune, 
~  which  rises  and  falls  the 

_   ,.     .  .  __  _  most  of  all  with  refer- 

FIG.  44.  —  Inclination  ana  Line  of  Nodes. 

ence  to  the  plane  of  the 

ecliptic,  would  never  be  more  than  a  third  of  an  inch  above 
or  below  the  level  of  the  paper. 

The  line  in  which  the  plane  of  a  planet's  orbit  cuts  the 
plane  of  the  earth's  orbit  at  the  ecliptic  is  called  the  Line  of 
Nodes.  Fig.  44  shows  how  the  line  of  nodes  and  the  inclina- 
tion of  the  two  orbits  are  related. 

225.  Geocentric  Motions  of  the  Planets;  i.e.,  their  motions 
with  respect  to  the  earth  regarded  as  the  centre  of  observation. 

While  the  planets  revolve  regularly  in  nearly  circular  orbits 
around  the  sun,  with  velocities *  which  depend  upon  their  dis- 
tance from  it,  the  motions  relative  to  the  earth  are  very  dif- 
ferent, being  made  up  of  the  planet's  real  motion  combined 

1 A  planet's  velocity  in  miles  per  second  equals  very  nearly 


225] 


DIRECT   AND   RETROGRADE   MOTION. 


163 


with,  the  apparent  motion  due  to  that  of  the  earth  in  her  own 
orbit. 

If,  for  instance,  we  keep  up  observations,  for  a  long  time,  of 
the  direction  of  Jupiter  as  seen  from  the  earth,  at  the  same 
time  watching  the  changes 
of  its  distance  by  measur- 
ing the  alterations  of  the 
planet's  apparent  size  as 
seen  in  the  telescope,  and 
then  plot  the  results  to  get 
the  form  of  the  orbit  of 
Jupiter  with  reference  to 
the  earth,  we  get  a  path 
like  that  shown  in  Fig.  45, 
which  represents  his  mo- 
tion relative  to  the  earth 
during  a  term  of  about 
twelve  years.  The  appear- 
ances are  all  the  same  as  if 
the  earth  were  really  at  rest  while  the  planet  moved  in  this 
odd  way. 

The  procedure  for  finding  this  relative  orbit  of  Jupiter  is  the  same 
as  that  indicated  in  Appendix,  Art.  428,  for  finding  the  form  of  the 
earth's  orbit  around  the  sun. 

226.  Direct  and  Retrograde  Motion.  —  With  the  eye  alone 
the  changes  in  a  planet's  diameter  would  not  be  visible,  and 
we  should  notice  only  the  alternating  direct  (eastward) 
and  retrograde  (westward)  motion  of  the  planet  among  the 
stars.  If  we  watch  one  of  the  planets  (say  Mars)  for  a  few 
weeks,  beginning  at  the  time  when  it  rises  at  sunset,  we  shall 
find  that  each  night  it  has  travelled  some  little  distance  to  the 
west ;  and  it  will  keep  up  this  westward  or  retrograde  motion 
for  some  weeks,  when  it  will  stop  or  become  "  stationary,"  and 
will  then  reverse  its  motion  and  begin  to  move  eastward.  If 


FIG.  45. 
Apparent  Geocentric  Motion  of  Jupiter. 


164 


ELONGATION   AND   CONJUNCTION. 


[§226 


we  watch  long  enough  (i.e.,  for  several  years)  we  shall  find 
that  it  keeps  up  this  oscillating  motion  all  the  time,  the  length 
of  its  eastward  swing  being  always  greater  than  that  of  the 
corresponding  westward  one.  All  the  planets,  without  excep- 
tion, behave  alike  in  this  respect,  as  to  their  alternate  direct 
and  retrograde  motion  among  the  stars. 

227.   Elongation    and    Conjunction.  —  The   visibility  of    a 
planet  does  not,  however,  depend  upon  its  position  among 


Conjunction 


Greatest  W.  Elongation 


Opposition 
FIG.  46. —Planetary  Configurations. 

the  stars,  but  upon  its  position  in  the  sky  with  reference  to 
the  sun's  place.  If  it  is  very  near  the  sun,  it  will  be  above 
the  horizon  only  by  day,  and  generally  we  cannot  see  it.  The 
Elongation  of  a  planet  is  the  apparent  distance  from  the  sun 
in  degrees,  as  seen  from  the  earth,  of  course.  In  Fig.  46,  for 
the  planet  P,  it  is  the  angle  PES.  When  the  planet  is  in  line 


§  227]  SYNODIC   PERIOD.  165 

with,  the  sun  as  seen  from  the  earth,  at  B,  C,  or  /  in  the  figure, 
the  elongation  is  zero,  and  the  planet  is  said  to  be  in  conjunc- 
tion; inferior  conjunction,  if  the  planet  is  between  the  earth 
and  the  sun,  as  at  /;  superior,  if  beyond  the  sun,  as  at  B  or  O. 
When  the  elongation  is  180°,  as  at  A,  the  planet  is  said  to  be 
in  opposition.  When  the  planet  is  at  an  elongation  of  90°,  as 
at  F  or  G,  it  is  in  quadrature.  Evidently  only  those  planets 
which  lie  within  the  earth's  orbit,  and  are  called  < inferior' 
planets,  can  have  an  inferior  conjunction;  and  only  those 
which  are  outside  the  earth's  orbit  (the  superior  planets)  can 
come  to  quadrature  or  opposition. 

228.  Synodic  Period.  —  The  synodic  period  of  a  planet  is 
the  time  occupied  by  it  in  passing  from  conjunction  to  con- 
junction again,  or  from  opposition  to  opposition;   so  called 
because  the  word  "  synod "  is  derived  from  two  Greek  words 
which  mean  '  a  coming  together.'     The  relation  of  the  synodic 
period  to  the  sidereal  is  the  same  for  planets  as  in  the  case  of 
the  moon.     If  E  is  the  length  of  the  true  (sidereal)  year,  and 
P  the  planet's  period,  S  being  the  length  of  the  synodic  period, 
then 

!=!_! 
SEP 

(The  difference  between  —  and  —  is  to  be  taken  without  regard 
E         P 

to  which  of  the  two  is  the  larger.) 

229.  The  Synodic  Motion,  or  Apparent  Motion  of  a  Planet 
with  respect  to  '  Elongation '  or  to  the  Sun's  Place  in  the  Sky. 

—  In  this  respect  there  is  a  marked  difference  between  the 
superior  and  inferior  planets. 

(a)  The  inferior  planets  are  never  seen  very  far  from  the 
sun,  but  appear  to  oscillate  back  and  forth  in  front  of  and 
behind  him.  Venus,  for  instance,  starting  at  superior  con- 
junction at  C  (Fig.  46),  seems  to  come  out  eastward  from  the 


166  PTOLEMAIC   AND  COPERNICAN   SYSTEMS.  [§  229 

sun  as  an  evening  star,  until,  at  the  point  V,  she  reaches  her 
greatest  eastern  elongation,  about  47°  from  the  sun.  Then  she 
begins  to  dimmish  her  elongation,  and  approaches  the  sun, 
until  she  comes  to  inferior  conjunction,  at  /.  From  there 
she  continues  to  move  westward  as  morning  star,  until  she 
comes  to  V,  her  greatest  western  elongation,  and  there  she 
begins  to  diminish  her  western  elongation  until,  at  the  end 
of  the  synodic  period,  she  is  back  at  superior  conjunction. 
The  time  taken  to  move  from  V'  to  V  through  C  is,  in  her 
case,  more  than  three  times  that  required  to  slide  back  from 
V  to  V  through  I.  The  gain  of  eastern  elongation  is  up-hill 
work,  as  she  is  then,  so  to  speak,  pursuing  the  sun,  which 
itself  moves  eastward  nearly  a  whole  degree  every  day  along 
the  ecliptic. 

(b)  The  superior  planets  may  be  found  at  all  elongations, 
and  do  not  oscillate  back  and  forth  with  reference  to  the 
apparent  place  of  the  sun,  but  continually  increase  their 
western  elongation  or  decrease  their  eastern.  They  always 
come  to  the  meridian  earlier  on  each  successive  night}  though  the 
difference  is  not  uniform. 

230.  Ptolemaic  and  Coperniean  Systems.  —  Until  the  time 
of  Copernicus  (about  1540)  the  Ptolemaic  System  prevailed 
unchallenged.  It  rejected  the  idea  of  the  earth's  rotation 
(though  Ptolemy  accepted  the  rotundity  of  the  earth),  placing 
her  at  the  centre  of  things  and  teaching  that  the  apparent 
motions  of  the  stars  and  planets  were  real  ones.  It  taught 
that  the  celestial  sphere  revolves  daily  around  the  earth,  carry- 
ing the  stars  and  planets  with  it,  and  that  besides  this  diurnal 
motion,  the  moon,  the  sun,  and  all  the  planets  revolve  around 
the  earth  within  the  sphere,  the  two  former  steadily,  but  the 
planets  with  the  peculiar  looped  motion  shown  in  Fig.  45. 

Copernicus  put  the  sun  at  the  centre,  and  made  the  earth 
revolve  on  its  axis  and  travel  around  the  sun,  and  showed  that 
it  was  possible  in  this  simple  way  to  account  for  all  the  other- 


§  230]  THE   PLANETS   THEMSELVES.  167 

wise  hopelessly  complicated  phenomena  of  the  planetary  and 
diurnal  motions,  so  far  as  then  known.  It  was  not  until  after 
the  invention  of  the  telescope,  and  the  introduction  of  new 
methods  of  observation,  that  the  facts  which  absolutely  demon- 
strate the  orbital  motion  of  the  earth  were  brought  to  light ; 
viz.,  Aberration  of  Light  (Appendix,  Art.  435)  and  Stellar 
Parallax  (Art.  433). 

THE   PLANETS   THEMSELVES. 

231.  In  studying  the  planetary  system  we  meet  a  number 
of  inquiries  which  refer  to  the  planet  itself  and  not  to  its 
orbit ;  relating,  for  instance,  to  its  magnitude;  its  mass,  density, 
and   surface-gravity;    its   diurnal   rotation   and   ellipticity ;   its 
brightness,  phases,  and  reflecting  power,  or  "  albedo  "  ;  the  pecul- 
iarities of  its  spectrum;  its  atmosphere;  its  surface-markings  and 
topography ;  and,  finally,  its  satellite  system. 

232.  Magnitude.  —  The  size  of  a  planet  is  found  by  measur- 
ing its  apparent  diameter  (in  seconds  of  arc)  with  some  form 
of   "micrometer"   (see  Appendix,  Art.   415).     Since  we   can 
find  the  distance  of  a  planet  from  the  earth  at  any  moment 
when  we  know  its  orbit,  this  micrometric  measure  will  give  us 
the  means  of  finding  at  once  the  planet's  diameter  in  miles. 

If  we  take  r  to  represent  the  number  of  times  by  which  the 
planet's  semi-diameter  exceeds  that  of  the  earth,  then  the  area 
of  the  planet's  surface  compared  with  that  of  the  earth  equals 
r2,  and  its  volume  or  bulk  equals  r3.  The  nearer  the  planet, 
other  things  being  equal,  the  more  accurately  r  and  the  quanti- 
ties to  be  derived  from  it  can  be  determined.  An  error  of  O'M 
in  measuring  the  apparent  diameter  of  Venus,  when  nearest  us, 
counts  for  less  than  thirteen  miles ;  while  in  Neptune's  case, 
the  same  error  would  correspond  to  more  than  1300  miles. 

233.  Mass,   Density,   and  Gravity.— If  the  planet  has  a 
satellite,  its  mass  is  very  easily  and  accurately  found  from  the 


168  THE  EOTATION   PERIOD.  [§  233 

following  proportion,  which  we  simply  state  without  demon- 
stration (see  General  Astronomy,  Arts.  536,  539)  j  viz. :  — 

AS     a3 

Mass  of  JSun :  mass  of  Planet : :  — 2 :  — , 

in  which  A  is  the  mean  distance  of  the  planet  from  the  sun  and 
T  its  sidereal  period  of  revolution,  while  a  is  the  distance  of 
the  satellite  from  the  planet,  and  t  its  sidereal  period ;  whence 

Mass  of  Planet  =  Sun  x  (—  X  —  \ 
\  t2      A3J 

Substantially  the  same  proportion  may  be  used  to  compare  the 
planet  with  the  earth ;  viz. :  — 

(Earth  +  Moon)  :  (Planet  +  Satellite)  : :  -\  :  ^L, 

t\       l* 

a^  and  <a  being  here  the  period  and  distance  of  the  moon,  and  a2  and 
tz  those  of  the  planet's  satellite. 

If  the  planet  has  no  satellite,  the  determination  of  its  mass  is  a  dif- 
ficult matter,  depending  upon  perturbations  produced  by  it  in  the 
motions  of  the  other  planets. 

Having  the  planet's  mass  compared  with  the  earth,  we  get 
its  density  by  dividing  the  mass  by  the  volume,  and  the  super- 
ficial gravity  is  found  by  dividing  by  r2  the  mass  of  the  planet 
compared  with  that  of  the  earth. 

234.  The  Rotation  Period  and  Data  connected  with  it.  — 

The  length  of  the  planet's  day,  when  it  can  be  determined  at 
all,  is  ascertained  by  observing  with  the  telescope  some  spot 
on  the  planet's  disc  and  noting  the  interval  between  its  returns 
to  the  same  apparent  position.  The  inclination  of  the  planet's 
equator  to  the  plane  of  its  orbit,  and  the  position  of  its  equi- 
noxes, are  deduced  from  the  same  observations  that  give  the 
planet's  diurnal  rotation ;  we  have  to  observe  the  path  pursued 
by  a  spot  in  its  motion  across  the  disc.  Only  Mars,  Jupiter, 
and  Saturn  permit  us  to  find  these  elements  with  any  consider- 
able accuracy. 

The  ellipticity  or  oblateness  of  the  planet,  due  to  its  rota- 


§  234]  SATELLITE   SYSTEM.  169 

tion,  is  found  by  taking  measures  of  its  polar  and  equatorial 
diameters. 

235.  Data    relating   to   the   Planet's   Light.  —  A   planet's 
brightness  and  its  reflecting  power,  or  "albedo,"  are  deter- 
mined by  photometric  observations,  and  the  spectrum  of  the 
planet's  light  is  of  course  studied  with  the  spectroscope.     The 
question  of  the  planet's  atmosphere  is  investigated  by  means  of 
various  effects  upon  the  planet's  appearance  and  light,  and  by 
the  phenomena  that  occur  when  the  planet  comes  very  near  to 
a  star  or  to  some  other  heavenly  body  which  lies  beyond.    The 
planet's  surface-markings  and  topography  are  studied  directly 
with  the  telescope,  by  making  careful  drawings  of  the  appear- 
ances noted  at  different  times.     Photography,  also,  is  begin- 
ning to  be  used  for  the  purpose.     If  the  planet  has  any  well- 
marked  and  characteristic  spots  upon  its  surface  by  which  the 
time  of  rotation  can  be  found,  then  it  soon  becomes  easy  to 
identify  such  as  are  really  permanent,  and  after  a  time  we  can 
chart  them  more  or  less  perfectly;  but  we  add  at  once  that 
Mars  is  the  only  planet  of  which,  so  far,  we  have  been  able  to 
make  anything  which  can  be  fairly  called  a  map. 

236.  Satellite   System.  —  The   principal   data  to  be  ascer- 
tained are  the  distances  and  periods  of  the  satellites.     These 
are  obtained  by  micrometric  measures  of  the  apparent  distance 
and  direction  of  each  satellite  from  the  planet,  followed  up  for 
a  considerable  time.     In  a  few  cases  it  is  possible  to  make 
observations  by  which  we  can  determine  the  diameters  of  the 
satellites,  and  when  there  are  a  number  of  satellites  together 
their  masses  may  sometimes  be  ascertained  from  their  mutual 
perturbations.     With  the  exception  of  our  moon  and  lapetus, 
the  outer  satellite  of  Saturn,  all  the  satellites  of  the  solar  sys- 
tem move  almost  exactly  in  the  plane  of  the  equator  of  the  planet 
to  which  they  belong ;  at  least,  so  far  as  known,  for  we  do  not 
know  with  certainty  the  position  of  the  equators  of  Uranus 


170  PLANETARY   DATA.  [§  236 

and  Neptune.  Moreover,  all  the  satellites,  except  the  moon 
and  Hyperion,  the  seventh  satellite  of  Saturn,  move  in  orbits 
that  are  practically  circular. 

237.  Tables  of  Planetary  Data.  —  In  the  Appendix  we  pre- 
sent tables  of  the  different  numerical  data  of  the  solar  system, 
derived  from  the  best  authorities  and  calculated  for  a  solar 
parallax  of  8".80,  the  sun's  mean  distance  being,  therefore, 
taken  as  92,897000  miles.     These  tabulated  numbers,  however, 
differ  widely  in  accuracy.     The  periods  of  the  planets  and 
their  distances  in  ' astronomical  units'  are  very  accurately 
known ;  probably  the  last  decimal  in  the  table  may  be  trusted. 
Next  in  certainty  come  the  masses  of  such  planets  as  have 
satellites,  expressed  in  terms  of  the  sun's  mass.     The  masses 
of  Venus  and  Mercury  are  much  more  uncertain. 

The  distances  of  the  planets  in  miles,  their  masses  in  terms 
of  the  earth's  mass,  and  their  diameter  in  miles,  all  involve  the 
solar  parallax,  and  are  affected  by  the  slight  uncertainty  in  its 
amount.  For  the  remoter  planets,  diameters,  volumes,  and 
densities  are  all  subject  to  a  very  considerable  percentage  of 
error.  The  student  need  not  be  surprised,  therefore,  at  finding 
serious  discrepancies  between  the  values  given  in  these  tables 
and  those  given  in  others,  amounting  in  some  cases  to  ten  or 
twenty  per  cent,  or  even  more.  Such  differences  merely  indi- 
cate the  actual  uncertainty  of  our  knowledge.  Fig.  47  gives 
an  idea  of  the  relative  sizes  of  the  planets. 

The  sun,  on  the  scale  of  the  figure,  would  be  about  a  foot  in 
diameter. 

238.  Sir  John  Herschel's  Illustration  of  the  Dimensions  of 
the   Solar   System.  —  In   his  "Outlines   of  Astronomy,"  Herschel 
gives  the  following  illustration  of  the  relative  magnitudes  and  dis- 
tances of  the  members  of  our  system  :  — 

"  Choose  any  well-levelled  field.  On  it  place  a  globe  two  feet  in  diame- 
ter. This  will  represent  the  sun.  Mercury  will  be  represented  by  a  grain 


RELATIVE   SIZE  OF  THE  PLANETS. 


171 


of  mustard  seed  on  the  circumference  of  a  circle  164  feet  in  diameter  for 
its  orbit ;  Venus,  a  pea,  on  a  circle  of  284  feet  in  diameter ;  the  Earth, 
also  a  pea,  on  a  circle  of  430  feet ;  Mars,  a  rather  large  pin's  head,  on  a 
circle  of  654  feet ;  the  asteroids,  grains  of  sand,  on  orbits  having  a  diame- 
ter of  1000  to  1200  feet ;  Jupiter,  a  moderate- sized  orange,  on  a  circle 
nearly  half  a  mile  across  ;  Saturn,  a  small  orange,  on  a  circle  of  four- fifths 


FIG.  47.  —  Relative  Size  of  the  Planets. 

of  a  mile  ;  Uranus,  a  full-sized  cherry  or  small  plum,  upon  a  circumfer- 
ence of  a  circle  more  than  a  mile  in  diameter ;  and,  finally,  Neptune,  a 
good-sized  plum,  on  a  circle  about  2|  miles  in  diameter." 

We  may  add  that,  on  this  scale,  the  nearest  star  would  be  on  the 
opposite  side  of  the  globe,  8000  miles  away. 

THE  TERRESTRIAL  PLANETS,  —  MERCURY,  VENUS,  AND 

MARS. 

239.  Mercury  has  been  known  from  the  remotest  antiquity, 
and  among  the  Greeks  it  had  for  a  time  two  names,  —  Apollo 
when  it  was  morning  star,  and  Mercury  when  it  was  evening 
star.  It  is  so  near  the  sun  that  it  is  comparatively  seldom 


172  MEBCTJR¥.  t§  239 


seen  with  the  naked  eye,  but  when  near  its  greatest  elongation 
it  is  easily  enough  visible  as  a  brilliant  reddish  star  of  the 
first  magnitude,  low  down  in  the  twilight.  It  is  best  seen  in 
the  evening  at  such  eastern  elongations  as  occur  in  the  spring. 
When  it  is  morning  star,  it  is  best  seen  in  the  autumn. 

It  is  exceptional  in  the  solar  system  in  various  ways.  It  is 
the  nearest  planet  to  the  sun,  receives  the  most  light  and  heat, 
is  the  swiftest  in  its  movement,  and  (excepting  some  of  the 
asteroids)  has  the  most  eccentric  orbit,  with  the  greatest  inclina- 
tion to  the  ecliptic.  It  is  also  the  smallest  in  diameter  (again 
excepting  the  asteroids),  has  the  least  mass,  and  (probably) 
the  greatest  density  of  all  the  planets. 

240.  Its  Orbit.  —  The  planet's  mean  distance  from  the  sun 
is  36,000000  miles,  but  the  eccentricity  of  its  orbit  is  so  great 
(0.205)  that   the   sun  is   7,500000   miles   out   of  the   centre, 
and  the  distance  ranges  all  the  way  from  281  millions  to  43^ 
millions,  while  the  planet's  velocity  in  the  different  parts  of 
its  orbit  varies  from  36  miles  a  second  to  only  23.     A  given 
area  upon  its  surface  receives  on  the  average   nearly  seven 
times  as  much  light  and  heat  as  it  would  on  the  earth  ;  but 
the  heat  received  when  the  planet  is  at  perihelion  is  2\  times 
greater  than  at  aphelion.     For  this  reason  there  must  be  at 
least  two  seasons  in  its  year,  due  to  the  changing  distance  of 
the  planet  from  the  sun,  whatever  may  be  the  position  of  its 
equator  or  the  length  of  its  day.     The  sidereal  period  is  88 
days,  and  the  synodic  period  (or  time  from  conjunction  to  con- 
junction) is  116  days.     The  greatest  elongation  ranges  from 
18°  to  28°,  and  occurs  about  22  days  before  and  after  the  in- 
ferior conjunction.     The  inclination  of  the  orbit  to  the  ecliptic 
is  about  7°. 

241.  Planet's  Magnitude,  Mass,  etc.  —  The  apparent  diam- 
eter of  Mercury  varies  from  5"  to  about  13",  according  to  its 
distance   from  us  ;   and  its  real  diameter  is  very  near   3000 


TELESCOPIC   APPEARANCE. 


173 


miles.  This  makes  its  surface  about  one-seventh  that  of  the 
earth,  and  its  bulk  or  volume  one-eighteenth.  The  planet's 
mass  is  very  difficult  to  determine,  since  it  has  no  satellite, 
and  it  is  not  accurately  known.  Probably  it  is  not  far  from 
one-fifteenth  of  the  earth's  mass  ;  it  is  certainly  smaller  than 
that  of  any  planet  (asteroids  ,  excepted).  Our  uncertainty  as 
to  the  mass  prevents  us  from  assigning  certain  values  to  its 
density  or  superficial  gravity,  though  it  is  probably  somewhat 
denser  than  the  earth,  and  the  force  of  gravity  upon  it  about 
one-half  what  it  is  upon  the  earth. 

242.   Telescopic  Appearances,   Phases,  etc.  —  Seen  through 
the   telescope  the  planet  looks   like   a  little  moon,  showing 


FIG.  48.  —  Phases  of  Mercury  and  Venus. 

phases  precisely  similar  to  those  of  our  satellite.  At  inferior 
conjunction  the  dark  side  is  towards  us  ;  at  superior  conjunc- 
tion the  illuminated  surface.  At  greatest  elongation,  the 
planet  appears  as  a  half-moon.  It  is  gibbous  between  superior 
conjunction  and  greatest  elongation,  while  between  inferior 
conjunction  and  greatest  elongation  it  is  crescent.  Fig.  48 
illustrates  these  phases. 

The  atmosphere  of  the  planet  cannot  be  as  dense  as  that  of 
the  earth  or  Venus,  because  at  a  transit  it  shows  no  encircling 
ring  of  light,  as  Venus  does  (Art.  248);  both  Huggins  and 
Vogel,  however,  report  that  the  spectrum  of  the  planet,  in 


174  DIURNAL   ROTATION   OF   MERCURY.  [§242 

addition  to  the  ordinary  dark  lines  belonging  to  the  spectrum 
of  reflected  sunlight,  shows  certain  bands  known  to  be  due  to 
water-vapor,  thus  indicating  that  water  exists  in  the  planet's 
atmosphere. 

Generally,  Mercury  is  so  near  the  sun  that  it  can  be  observed 
only  by  day ;  but  when  proper  precautions  are  taken  to  screen 
the  object-glass  of  the  telescope  from  direct  sunlight,  the  ob- 
servation is  not  especially  difficult.  The  surface  presents  very 
little  of  interest.  The  disc  is  brighter  at  the  edge  than  at  the 
centre,  but  the  markings  are  not  well  enough  denned  to  give 
us  any  really  satisfactory  information  as  to  its  topography. 

The  albedo,  or  reflecting  power,  of  the  planet  is  very  low, 
only  0.13,  somewhat  inferior  to  that  of  the  moon  and  very 
much  below  that  of  any  other  of  the  planets.  No  satellite  is 
known,  and  there  is  no  reason  to  suppose  that  it  has  any. 

243.  Diurnal  Rotation  of  the  Planet.  —  In  1889,  Schiaparelli, 
the  Italian  astronomer,  announced  that  he  had  discovered  cer- 
tain markings  upon  the  planet,  and  that  they  showed  that  the 
planet  rotates  on  its  axis  only  once  during  its  orbital  period  of 
eighty-eight  days,  thus   keeping  the  same  face  always  turned 
towards  the  sun,  in  the  same  way  that  the  moon  behaves  with 
respect  to  the  earth.     Owing  to  the  eccentricity  of  the  planet's 
orbit,  however,   it   must    have   a  large   libration   (Art.    145), 
amounting  to  about  23£°  on  each  side  of  the  mean ;  i.e.,  seen 
from  a  favorable   station   on  the  planet's  surface,   the   sun, 
instead  of  rising  and  setting,  as  with  us,  would  seem  to  oscil- 
late back  and  forth  through  an  arc  of  47°  once  in  88  days. 

This  asserted  discovery  is  very  important  and  has  excited 
great  interest.  Schiaparelli  is  probably  correct,  but  it  may  be 
well  to  wait  for  confirmation  of  his  observations  by  others 
before  absolutely  accepting  the  conclusion. 

244.  Transits  of  Mercury.  —  At  the  time  of  inferior  con- 
junction, the  planet  usually  passes  north  or  south  of  the  sun; 


§  244]  VENUS.  175 

the  inclination  of  its  orbit  being  7°;  but  if  the  conjunction 
occurs  when  the  planet  is  very  near  its  node  (Art.  224),  it 
crosses  the  sun's  disc  and  becomes  visible  upon  it  as  a  small 
black  spot ;  not,  however,  large  enough  to  be  seen  without  a 
telescope,  as  Venus  can  under  similar  circumstances.  Since 
the  earth  passes  the  planet's  line  of  nodes  on  May  7th  and 
Nov.  9th,  transits  can  occur  only  near  those  days. 

The  transits  of  the  last  half  of  the  present  century  are  as  follows  : 
May  Transits.  —  May  6th,  1878;  May  9th,  1891 ;  — visible  in  the 
United  States.  November  Transits.  — Nov.  12th,  1861;  Nov.  5th, 
1868;  Nov.  7th,  1881;  Nov.  10th,  1894. 

Transits  of  Mercury  are  of  no  particular  astronomical  importance, 
except  as  furnishing  accurate  determinations  of  the  planet's  place  in 
the  sky  at  a  given  time. 


VENUS. 

245.  The  second  planet  in  order  from  the  sun  is  Venus,  the 
brightest  and  most  conspicuous  of  all.  It  is  so  brilliant  that 
at  times  it  casts  a  shadow,  and  is  easily  seen  by  the  naked  eye 
in  the  daytime.  Like  Mercury  it  had  two  names  among  the 
Greeks,  —  Phosphorus  as  morning  star,  and  Hesperus  as  even- 
ing star. 

Its  mean  distance  from  the  sun  is  67,200000  miles,  and  its 
distance  from  the  earth  ranges  from  26,000000  miles  (93  —  67) 
to  160,000000  (93  +  67).  No  other  body  ever  comes  so  near 
the  earth  except  the  moon,  and  occasionally  a  comet.  The 
eccentricity  of  the  orbit  of  Venus  is  the  smallest  in  the  plane- 
tary system,  only  0.007,  so  that  the  greatest  and  least  dis- 
tances of  the  planet  from  the  sun  differ  from  the  mean  less 
than  500,000  miles.  Its  sidereal  period  is  225  days,  or  seven 
and  a  half  months  ;  and  its  synodic  period  584  days,  —  a  year 
and  seven  months.  From  superior  conjunction  to  greatest 
elongation  is  only  71  days.  The  inclination  of  its  orbit  is  not 
quite  3y,  —  less  than  half  that  of  Mercury. 


176  MAGNITUDE,   MASS,   ETC.  t§  2^ 

246.  Magnitude,  Mass,  Density,  etc. —  The  apparent  diam- 
eter of  the  planet  varies  from  67",  at  the  time  of  inferior  con- 
junction, to  only  11",  at  superior  ;  the  great  difference  arising 
from  the  enormous  variation  in  the  distance  of  the  planet  from 
the  earth.     The  real  diameter  of  the  planet  in  miles  is  about 
7700.     Its  surface  compared  with  that  of  the  earth  is  T9^ ;  its 
volume,  -j^.     By  means  of  the  perturbations  she  produces 
upon  the  earth,  the  mass  of  Venus  is  found  to  be  a  little  less 
than  four-fifths  of  the  earth's  mass,  so  that  her  mean  density 
is  a  little  less  than  the  earth's.     In  magnitude   she   is   the 
earth's  twin  sister. 

247.  General   Telescopic  Appearance ;    Phases,   etc.  —  The 

general  telescopic  appearance  of  Venus  is  striking  on  account 
of  her  great  brilliancy,  but  exceedingly  unsatisfactory  because 
nothing  is  distinctly  outlined  upon  the  disc. 

When  about  midway  between  greatest  elongation  and  infe- 
rior conjunction,  the  planet  has  an  apparent  diameter  of  40", 
so  that  with  a  magnifying  power  of  only  45  she  looks  exactly 
like  the  moon  four  days  old,  and  of  the  same  apparent  size. 
(Very  few  persons,  however,  would  think  so  on  the  first  view 
through  the  telescope;  the  novice  always  underrates  the 
apparent  size  of  a  telescopic  object.) 

The  phases  of  Venus  were  first  discovered  by  Galileo  in  1610,  and 
afforded  important  evidence  as  to  the  truth  of  the  Copernican  system 
as  against  the  Ptolemaic.  Fig.  49  represents  the  planet's  disc  as  seen 
at  five  points  in  its  orbit.  1,  3,  and  5  are  taken  at  superior  conjunc- 
tion, greatest  elongation,  and  near  inferior  conjunction,  respectively; 
while  2  and  4  are  at  intermediate  points.  (No.  2  is  badly  engraved, 
however ;  the  sharp  corners  are  impossible.) 

The  planet  attains  its  maximum  brightness  when  its  appar- 
ent area  is  at  a  maximum,  about  thirty-six  days  before  and 
after  inferior  conjunction.  According  to  Zollner,  the  '  albedo ' 
of  the  planet  is  0.50;  i.e.,  it  reflects  about  half  the  light 
which  falls  upon  it,  the  reflecting  power  being  about  three 


247] 


TELESCOPIC  APPEARANCES  OF  VENUS. 


177 


times  that  of  the  moon,  and  almost  four  times  that  of  Mer- 
cury. It  is,  however,  slightly  exceeded  by  the  reflecting 
power  of  Uranus  and  Jupiter,  while  that  of  Saturn  is  about 


FIG.  49.  —  Telescopic  Appearances  of  Venus. 

the  same.  This  high  albedo  probably  indicates  a  surface 
mostly  covered  with  clouds,  since  few  rocks  or  soils  could 
match  its  brightness.  Like  Mercury,  Mars,  and  the  moon,  the 
disc  of  Venus  is  brightest  at  the  edge,  —  in  contrast  with  the 
appearance  of  Jupiter  and  Saturn. 

248.  Atmosphere  of  the  Planet. — When  the  planet  is  near 
inferior  conjunction,  the  horns  of  the  crescent  extend  notably 
beyond  the  diameter ;  and  when  very  near  conjunction,  a  thin 
line  of  light  has  been  seen  by  some  observers  to  complete  the 
whole  circumference  of  the  disc.  This  is  due  to  the  refrac- 
tion of  sunlight  bent  around  the  planet's  globe  by  its  atmos- 
phere, a  phenomenon  still  better  seen  when  the  planet  is 
entering  upon  the  sun's  disc  at  a  transit.  The  black  disc  is 


178 


ATMOSPHERE   OP  VENUS. 


[§248 


then  encircled  by  a  delicate  luminous  ring,  as  illustrated  by 
Fig.  50.     The  planet's  atmosphere  is  probably  from  one  and 

one-half  to  two  times  as 
dense  as  our  own,  and 
the  spectrum  shows 
evidence  of  water-va- 
por in  it.  Many  ob- 
servers have  also  re- 
ported faint  lights  as 
visible  at  times  on  the 
dark  portions  of  the 
planet's  disc.  These 
cannot  be  accounted 
for  by  any  mere  reflec- 
tion or  refraction  of 
sunlight,  but  must  orig- 
inate on  the  planet  it- 
self. They  recall  the 
Aurora  Borealis  and 
other  electrical  mani- 
festations on  the  earth,  though  it  is  impossible  to  give  a  certain 
explanation  of  them  as  yet. 

249.  Surface-markings,  Rotation,  etc. — As  has  been  said, 
Venus  is  a  very  unsatisfactory  telescopic  object.  She  pre- 
sents no  obvious  surface-markings,  —  nothing  but  occasional 
indefinite  shadings :  sometimes,  however,  when  in  the  crescent 
phase,  intensely  bright  spots  have  been  reported  near  the 
points  of  the  crescent,  which  may  perhaps  be  "  ice-caps  "  like 
those  which  are  seen  on  Mars.  The  darkish  shadings  may 
possibly  be  continents  and  oceans,  dimly  visible,  or  they  may 
be  atmospheric  objects ;  observations  do  not  yet  decide.  From 
certain  irregularities  occasionally  observed  upon  the  "termi- 
nator "  (Art.  146),  various  observers  have  concluded  that  there 
are  high  mountains  upon  the  planet. 


FIG.  50.  —  Atmosphere  of  Venus  as  seen  during  a 
Transit.     (Vogel,  1882.) 


§  249]  TRANSITS.  179 

As  to  the  rotation-period  of  the  planet,  nothing  is  yet  cer- 
tainly known.  The  length  of  its  day  has  been  set,  on  very 
insufficient  grounds,  at  about  23  hours  and  21  minutes  ;  but  the 
recent  work  of  Schiaparelli  makes  it  quite  certain  that  this 
result  cannot  be  trusted,  and  renders  it  rather  probable  that 
Venus  behaves  like  Mercury  in  its  diurnal  rotation,  the  length 
of  its  sidereal  day  being  equal  to  the  time  of  its  orbital  revolu- 
tion. The  planet's  disc  shows  no  sensible  oblateness. 

No  satellite  has  ever  been  discovered;  not,  however,  for 
want  of  earnest  searching. 

250.  Transits.  —  Occasionally  Venus  passes  between  the 
earth  and  the  sun  at  inferior  conjunction,  giving  us  a  so- 
called  "transit."  She  is  then  visible,  even  to  the  naked  eye, 
as  a  black  spot  on  the  sun's  disc,  crossing  it  from  east  to  west. 
When  the  transit  is  central  it  occupies  about  eight  hours,  but 
when  the  track  lies  near  the  edge  of  the  disc  the  duration 
is  correspondingly  shortened.  Since  the  earth  passes  the 
nodes  of  the  orbit  on  June  5th  and  Dec.  7th,  all  the  transits 
occur  near  these  days,  but  they  are  ex- 
tremely rare  phenomena.  Their  special 
interest  consists  in  their  availability  for 
the  purpose  of  finding  the  sun's  parallax 
(see  Appendix,  Art.  437,  and  General 
Astronomy,  Chap.  XVI.). 

The  first  observed  transit  in  1639  was  seen 
by  only  two  persons,  —  Horrox  and  Crabtree  in  FlG-  51> 

England, -but  the  four  which  have  occurred  n 
since  then  have  been  observed  in  all  parts  of  the  world  by  scientific 
expeditions  sent  out  for  the  purpose  by  the  different  governments. 
The  transits  of  1869  and  1882  were  visible  in  the  United  States. 
Transits  of  Venus  have  occurred  or  will  occur  at  the  following 
dates :  — 

(  Dec.  7th,  1631.  <  June  5th,  1761. 

1  Dec.  4th,  1639.  (  June  3d,    1769. 


180  MARS.  [§  250 

5  Dec.  9th,  1874.  (  June  8th,  2004. 

(  Dec.  6th,  1882.  <  June  6th,  2012. 

Fig.  51  shows  the  tracks  of  Venus  across  the  sun's  disc  in  the  tran- 
sits of  1874  and  1882. 


MARS. 

251.  This  planet,  also,  has  always  been  known.  It  is  so 
conspicuous  on  account  of  its  fiery  red  color  and  brightness, 
as  well  as  the  rapidity  and  apparent  capriciousness  of  its 
movement  among  the  stars,  that  it  could  not  have  escaped  the 
notice  of  the  very  earliest  observers. 

Its  mean  distance  from  the  sun  is  a  little  more  than  one  and 
a  half  times  that  of  the  earth  (141,500000  miles),  and  the  ec- 
centricity of  its  orbit  is  so  considerable  (0.093)  that  its  radius 
vector  varies  more  than  26,000000  miles.  At  opposition  the 
planet's  average  distance  from  the  earth  is  48,600000  miles ; 
but  when  opposition  occurs  near  the  planet's  perihelion,  this 
distance  is  reduced  to  less  than  36,000000  miles,  while  near 
aphelion  it  is  over  61,000000  miles.  At  conjunction  the  aver- 
age distance  from  the  earth  is  234,000000  miles. 

The  apparent  diameter  and  brightness  of  the  planet  of 
course  vary  enormously  with  these  great  changes  of  distance. 
At  a  favorable  opposition  (when  the  planet's  distance  from  us 
is  the  least  possible)  it  is  more  than  fifty  times  as  bright  as  at 
conjunction,  and  fairly  rivals  Jupiter;  when  most  remote,  it  is 
hardly  as  bright  as  the  Pole-star. 

The  favorable  oppositions  occur  always  in  the  latter  part  of  August, 
and  at  intervals  of  fifteen  or  seventeen  years.  The  last  such  opposi- 
tion was  in  1877,  and  the  next  will  be  in  1892. 

The  inclination  of  the  orbit  is  small,  1°  51'.  The  planet's 
sidereal  period  is  687  days  (one  year,  ten  and  a  half  months)  j 
its  synodic  period  is  much  the  longest  in  the  planetary  system, 
being  780  days,  or  nearly  two  years  and  two  months.  During 


§251]  TELESCOPIC   ASPECT.  181 

710  of  these  780  days  it  moves  towards  the  east,  and  retro- 
grades during  70. 

252.  Magnitude,  Mass,  etc.  —  The  apparent  diameter  of  the 
planet  ranges  from  3".6,  at  conjunction,  to  25"  at  a  favorable 
opposition.     Its  real  diameter  is  very  closely  4230  miles,  with 
an   error  of   perhaps  20  miles  one  way  or  the  other.     This 
makes   its   surface   about   two-sevenths,  and   its   volume  one- 
seventh  of  the  earth's.     Its  mass  is  a  little  less  than  one-ninth 
of  the  earth's  mass.    This  makes  its  density  0.73,  and  its  super- 
ficial gravity  0.38 ;  i.e.,  a  body  which  here  weighs  100  pounds 
would  have  a  weight  of  only  38  pounds  on  the  surface  of  Mars. 

253.  General  Telescopic  Aspect,   Phases,   etc. — When  the 
planet  is  nearest,  it  is  more  favorably  situated  for  telescopic 
observation  than  any  other  heavenly  body,   the   moon   alone 
excepted.      It  then  shows  a  ruddy  disc, 

which,  with  a  magnifying  power  of  75, 
is  as  large  as  the  moon.  Since  its  orbit 
is  outside  the  earth's,  it  never  exhibits 
the  crescent  phases  like  Mercury  and 
Venus ;  but  at  quadrature  it  appears 
distinctly  gibbous,  as  in  Fig.  52,  about 
like  the  moon  three  days  from  full.  Like 
Mercury,  Venus,  and  the  moon,  its  disc 
is  brightest  at  the  limb  (i.e..  at  its  circu- 

Mars  at  Quadrature. 

lar  edge)  ;  but  at  the  "  terminator,"  or 
boundary  between  day  and  night  upon  the  planet's  surface, 
there  is  a  slight  shading,  which,  taken  in  connection  with  cer- 
tain other  phenomena,  indicates  the  presence  of  an  atmosphere. 
This  atmosphere,  however,  is  probably  much  less  dense  than 
that  at  the  earth,  as  indicated  by  the  infrequency  of  clouds 
and  of  other  atmospheric  phenomena  familiar  to  us  on  the 
earth.  Huggins  reports,  however,  that  the  planet's  spectrum 
shows  the  lines  of  water-vapor. 


182  MARS.  [§253 

Zollner  gives  the  albedo  of  Mars  as  0.26,  just  double  that  of 
Mercury,  and  much  higher  than  that  of  the  moon,  but  only 
about  half  that  of  Venus  and  the  major  planets.  Near  oppo- 
sition the  brightness  of  the  planet  suddenly  increases  in  the 
same  way  as  that  of  the  moon  near  the  full  (Art.  149). 

254.  Rotation,    etc.  —  The    spots  upon  the  planet's   disc 
enable  us  to  determine  its  period  of  rotation  with  great  pre- 
cision.    Its  sidereal  day  is  found  to  be  24  hours,  37  minutes, 
22.67  seconds,  with  a  probable  error  not  to  exceed  one-fiftieth 
of  a  second.     It  is  the  only  one  of  the  planets  which  has  the 
length  of  its  day  determined  with  any  such  accuracy.     The4 
exactness  is  obtained  by  comparing  the  drawings  of  the  planet 
made  two  hundred  years  ago  with  others  made  recently. 

The  inclination  of  the  planet's  equator  to  the  plane  of  its 
orbit  is  very  nearly  24°  50f  (26°  21'  to  the  ecliptic).  So  far, 
therefore,  as  depends  upon  that  circumstance,  Mars  should 
have  seasons  substantially  the  same  as  our  own,  and  certain 
phenomena  make  it  evident  that  such  is  the  case. 

The  planet's  rotation  causes  a  slight  flattening  of  the  poles, 
—  about  Y^-Q-,  according  to  the  latest  determinations.  (Larger 
values,  now  known  to  be  erroneous,  are  given  in  many  text- 
books.) 

255.  Surface  and  Topography. — With  even  a  small  tele- 
scope, not  more  than  four  or  five  inches  in  diameter,  the  planet 
is  a  very  beautiful  object,  showing  a  surface  diversified  with 
markings,  light  and  dark,  which  for  the  most  part  are  found  to 
be  permanent.     Occasionally,  however,  we  see  others  of  a  tem- 
porary character,  supposed  to  be  clouds;   but  these  are  sur- 
prisingly rare,  compared  with   clouds   upon  the  earth.     The 
permanent  markings  are  broadly  divisible  into  three  classes  :  — 

First,  the  white  patches,  two  of  which  are  specially  con- 
spicuous near  the  planet's  poles,  and  are  generally  supposed 
to  be  masses  of  snow  or  ice,  since  they  behave  just  as  would 


§  255]  SCHIAPARELLI'S   OBSERVATIONS.  183 

be  expected  if  such  were  the  case.  The  northern  one  dwin- 
dles away  during  the  northern  summer,  when  the  north  pole  is 
turned  towards  the  sun,  while  the  southern  one  grows  rapidly 
larger ;  and  vice  versa  during  the  southern  summer. 

Second)  patches  of  bluish  gray  or  greenish  shade,  covering 
about  three-eighths  of  the  planet's  surface,  and  generally  sup- 
posed to  be  bodies  of  water. 

Third,  extensive  regions  of  various  shades  of  orange  and 
yellow,  covering  nearly  five-eighths  of  the  surface,  and  inter- 
preted as  land. 

These  markings,  of  course,  are  best  seen  when  near  the 
centre  of  the  planet's  disc ;  near  the  limb  they  are  lost  in  the 


FIG.  53.  —  Telescopic  Views  of  Mars. 

brilliant  light  which  there  prevails,  and  at  the  terminator  they 
fade  out  in  the  shade.  Fig.  53  gives  an  idea  of  the  planet's 
general  appearance,  though  without  pretending  to  minute 
accuracy. 

256.  Schiaparelli's  Observations.  —  In  addition  to  these  three 
classes  of  markings,  the  Italian  astronomer,  Schiaparelli,  reports  the 
observation  of  a  net-work  of  fine,  straight,  dark  lines,  or  "  canals,"  as 
he  calls  them,  crossing  the  "  continents  "  in  every  direction.  He  is  so 
careful  and  experienced  an  observer  that  his  results  cannot  be  lightly 
rejected ;  and  yet  it  is  not  easy  to  banish  a  vague  suspicion  of  some 
error  or  illusion,  partly  because  his  observations  have  thus  far  received 
so  little  confirmation  from  others,  and  partly  because  his  "canals" 
are  so  difficult  to  explain.  They  can  hardly  be  rivers,  because  they 


184  SCHIAPAKtiLLl's   OBSERVATIONS.  [§  2^6 

are  quite  straight;  nor  can  they  be  artificial  waterways,  since  the 
narrowest  of  them  are  at  least  100  miles  wide.  To  add  to  the  mys- 
tery, he  finds  that  at  certain  times  many  of  them  become  "  doubled," 
—  the  two  which  replace  the  former  single  one  running  parallel  to 
each  other  sometimes  for  thousands  of  miles,  with  a  space  of  200  or 
300  miles  between  them;  and  this  "gemination"  seems  to  follow  the 
course  of  the  planet's  seasons.  No  satisfactory  explanation  for  such 
phenomena  appears  as  yet. 

Schiaparelli  and  some  other  observers  report  also,  within  a  year  or 
two,  certain  phenomena  which  look  as  if  large  regions  of  land  were 
subject  to  periodic  inundations.  It  is  hoped  that  in  1892  the  great 
telescopes  of  the  world  will  throw  some  light  on  these  peculiar  prob- 
lems; and  possibly  photography  may  take  a  hand  in  the  affair  by 
that  time. 

257.  Maps  of  the  Planet.  —  A  number  of  maps  of  Mars  have 
been  constructed  by  different  observers  since  the  first  one  was  made 
by  Maedler  in  1830.    Fig.  54  is  reduced  from  one  which  was  published 
in  1888  by  Schiaparelli,  and  shows  most  of  his  "canals"  and  their 
"  geminations."    While  there  may  be  some  doubt  as  to  the  accuracy 
of  the  minor  details,  there  can  be  no  doubt  that  the  main  features  of 
the  planet's  surface  are  substantially  correct.      The  nomenclature, 
however,  is  in  a  very  unsettled  state.     Schiaparelli  has  taken  his 
names  mostly  from  ancient  geography,  while  the  English  areogra- 
phers,1  following  the  analogy  of  the  lunar  maps,  have  mainly  used  the 
names  of  astronomers  who  have  contributed  to  our  knowledge  of  the 
planet's  surface. 

If  the  prevailing  interpretations  of  the  markings  upon  the  planet 
are  correct,  it  is  certain  that  the  temperature  of  Mars  must  be  higher 
than  that  of  the  earth,  notwithstanding  his  smaller  supply  of  solar 
heat  (somewhat  less  than  half) .  Otherwise,  the  snow  and  ice  in  the 
winter  would  not  be  limited  to  mere  polar  caps,  but  would  extend  far 
into  the  lower  latitudes,  as  they  do  upon  the  earth. 

258.  Satellites.  —  The  planet  has  two  satellites,  discovered 
by  Professor  Hall,  at  Washington,  in  1877.     They  are  ex- 

lrThe  Greek  name  of  Mars  is  Ares;  hence  " Areography  "  is  the  de- 
scription of  the  surface  of  Mars. 


258] 


CHART   OF   MARS. 


185 


186  HABITABILITY   OF   MARS.  [§  258 

tremely  small,  and  observable  only  with  very  large  telescopes. 
The  outer  one,  Deiinos,  is  at  a  distance  of  14,600  mi]es  from 
the  planet's  centre,  and  has  a  sidereal  period  of  30  hours,  18 
minutes  ;  while  the  inner  one,  Phobos,  is  at  a  distance  of  only 
5800  miles,  and  its  period  is  only  7  hours,  39  minutes,  —  less 
than  one-third  of  the  planet's  day.  (This  is  the  only  case  of  a 
satellite  with  a  period  shorter  than  the  day  of  its  primary.) 
Owing  to  this  circumstance,  it  rises  in  the  west,  as  seen  from 
the  planet's  surface,  and  sets  in  the  east,  completing  its 
strange,  backward,  diurnal  revolution  in  about  eleven  hours. 
Deimos,  on  the  other  hand,  rises  in  the  east,  but  takes  nearly 
132  hours  in  its  diurnal  circuit,  which  is  more  than  four  of  its 
months.  Both  the  Orbits  are  sensibly  circular,  and  lie  very 
closely  in  the  plane  of  the  planet's  equator. 

Micrometric  measures  of  the  diameters  of  such  small  objects  are  im- 
possible; but  from  photometric  observations,  Professor  E.  C.  Pick- 
ering, assuming  that  they  have  the  same  reflecting  power  as  that  of 
Mars  itself,  estimates  the  diameter  of  Phobos  as  about  seven  miles, 
and  that  of  Deimos  as  five  or  six.  According  to  this,  Phobos,  at  the 
time  of  full  moon,  as  seen  from  the  planet's  surface,  would  have  an 
apparent  diameter  of  about  one-fifth  that  of  our  moon,  and  would 
probably  give  about  one-fiftieth  as  much  light.  Deimos  would  be 
hardly  more  than  a  brilliant  star,  like  Venus. 

259.  Habitability  of  Mars.  —  As  to  this  question,  we  can  only 
say  that,  while  the  conditions  on  Mars  are  very  different  from  those 
prevailing  on  the  earth,  the  difference  is  less  than  in  the  case  of  any 
other  heavenly  body  with  which  we  are  acquainted ;  and  if  life,  such 
as  we  know  life  upon  the  earth,  can  exist  anywhere  else,  Mars  is  the 
place.  But  there  is  at  present  no  scientific  ground  for  belief  one  way 
or  the  other  as  to  the  habitability  of  "  other  worlds  than  ours,"  pas- 
sionately as  the  doctrine  has  been  affirmed  and  denied  by  men  of 
opposite  opinions. 


260]  THE   ASTEROIDS.  187 


CHAPTER   IX. 

THE   PLANETS   CONTINUED. 

THE  ASTEROIDS.  —  INTRA-MERCURIAN  PLANETS  AND  THE 
ZODIACAL  LIGHT.  —  THE  MAJOR  PLANETS,  JUPITER, 
SATURN,  URANUS,  AND  NEPTUNE. 

THE   ASTEROIDS,   OR   MINOR   PLANETS. 

260.  THE  asteroids1  are  a  multitude  of  small  planets  cir- 
cling around  the  sun  in  the  space  between  Mars  and  Jupiter. 
It  was  early  noticed  that  between  Mars  and  Jupiter  there  is  a 
gap  in  the  series  of  planetary  distances,  and  when  Bode's  Law 
(Art.  219)  was  published  in  1772,  the  impression  became  very 
strong  that  there  must  be  a  missing  planet  in  the  space,  —  an 
impression  greatly  strengthened  when  Uranus  was  discovered 
in  1781,  at  a  distance  precisely  corresponding  to  that  law. 

The  first  member  of  the  group  was  found  by  the  Sicilian  as- 
tronomer, Piazzi,  on  the  very  first  night  of  the  present  century 
(Jan.  1,  1801).  He  named  it  Ceres,  after  the  tutelary  divinity 
of  Sicily.  The  next  year  Pallas  was  discovered  by  Olbers. 
Juno  was  found  in  1804  by  Harding,  and  in  1807  Olbers,  who 
had  broached  the  theory  of  an  exploded  planet,  discovered  the 
fourth,  Vesta,  the  only  one  which  is  bright  enough  ever  to  be 
easily  seen  by  the  naked  eye.  The  search  was  kept  up  for 
some  years  longer,  but  without  success,  because  the  searchers 

1  They  were  first  called  "asteroids"  (i.e.,  "star-like"  bodies)  by  Sir 
William  Herschel  early  in  the  century,  because,  though  really  planets, 
the  telescope  shows  them  only  as  stars,  without  a  sensible  disc. 


188  ORBITS   OF  THE  ASTEROIDS.  [§  26^ 

did  not  look  for  small  enough  objects.  The  fifth  asteroid 
(Astraea)  was  found  in  1845  by  Hencke,  an  amateur  who  had 
resumed  the  subject  afresh  by  studying  the  smaller  stars.  In 
1847  three  more  were  discovered,  and  every  year  since  then 
has  added  from  one  to  twenty.  '  In  November,  1890,  the  list 
included  300.  They  all  have  names,  but  more  generally  they 
are  designated  by  numbers  in  the  order  of  their  discovery. 
Thus,  Ceres  is  ©,  Thule  is  (279),  etc. 

Of  the  300,  113  were  discovered  in  Germany,  80  in  France,  76 
in  the  United  States,  20  by  English  observers,  and  11  by  Italians. 

Palisa,  who  stands  far  ahead  of  all  the  other  planet-hunters,  is  alone 
responsible  for  71  of  them,  and  the  late  Dr.  Peters  of  Clinton,  N.Y., 
for  48.i 

261.  Their  Orbits.  —  The  mean  distances  of  the  different 
asteroids  from  the  sun  differ  pretty  widely,  and  the  periods,  of 
course,  correspond.  Medusa,  (UQ),  is  the  nearest  to  the  sun  of 
those  at  present  known,  its  distance  being  2.13  (astronomical 
units),  or  198,000000  miles,  with  a  period  of  3  years  and  40 
days.  Thule,  (279),  is  the  most  remote,  with  a  mean  distance 
of  4.30  (400,000000  miles)  and  a  period  only  10  days  less  than 
9  years. 

The  inclinations  of  the  orbits  to  the  ecliptic  average  nearly 
8°.  The  orbit  of  Pallas,  @,  is  inclined  at  an  angle  of  35°, 
and  seven  others  exceed  25°.  The  eccentricity  of  the  orbits  is 
very  large  in  many  cases.  Aethra,  (132),  has  the  largest  eccen- 
tricity (0.38),  and  ten  others  have  an  eccentricity  exceeding 
0.30. 


1  These  figures  are  from  the  lists  given  in  the  Annuaire  du  Bureau  des 
Longitudes.  Other  lists  differ  somewhat  in  the  assignment  of  the  discov- 
eries, as  there  are  a  number  of  cases  where  the  same  planet  has  been  dis- 
covered independently,  and  almost  simultaneously,  by  more  than  one 
observer. 


§  262]  THE   BODIES   THEMSELVES.  189 

262.  The  Bodies   Themselves. — The   four  first  discovered, 
and  one  or  two  others,  when  examined  with  a  powerful  tele- 
scope, show  a  perceptible  disc,  not  large  enough,  however,  for 
accurate  measurement.     By  photometric  observations,  assum- 
ing—  what   is   by   no   means   certain  —  that  their  albedo   is 
about  the  same  as  that  of  Mars,  it  is  estimated  that  Vesta,  the 
largest  and  brightest,  has  a  diameter  of  about  320  miles.     The 
other  three  of  the  first  four  may  be  two-thirds  as  large.     None 
of  the  rest  can  well  exceed  100  miles  in  diameter;  and  the 
more  newly  discovered  ones,  which  are  just  fairly  visible  in  a 
telescope  with  an  aperture  of  10  or  12  inches,  cannot  be  many 
times   larger  than  the  moons  of   Mars,  —  say  from  10  to  20 
miles  in  diameter. 

As  to  the  individual  masses  and  densities,  we  have  no  certain 
knowledge. 

Assuming  that  the  density  of  Vesta  is  about  the  same  as  that  of 
the  rocks  which  compose  the  earth's  crust,  her  mass  may  be  as  great 
3(8  strVffo  that  of  the  earth.  If  so,  gravity  on  her  surface  would  be  about 
^  of  gravity  here,  so  that  a  body  would  fall  about  six  inches  in  the 
first  second.  Of  course,  on  the  smaller  asteroids  it  would  be  much 
less. 

From  the  perturbations  of  Mars,  Leverrier  has  estimated 
that  the  aggregate  mass  of  the  whole  swarm  cannot  exceed 
one-fourth  the  mass  of  the  earth,  — •  something  more  than  double 
that  of  Mars. 

The  united  mass  of  those  at  present  known  would  make  only  a 
small  fraction  of  such  a  body,  —  hardly  a  thousandth  of  it;  prob- 
ably, however,  those  still  undiscovered  are  very  numerous. 

263.  Origin.  —  As   to  this  we   can  only  speculate.     It  is 
hardly  possible  to  doubt,  however,  that  this  swarm  of  little 
rocks  in  some  way  represents  a  single  planet  of  the  "  terres- 
trial" group.     A  commonly  accepted  view  is  that  the  mate- 
rial, which,  according  to  the  nebular  hypothesis,  once  formed 


190  INTRA-MERCTJRIAN  PLANETS.  [§263 

a  ring  (like  one  of  the  rings  of  Saturn),  and  ought  to  have  col- 
lected to  make  a  single  planet,  has  failed  to  be  so  united ;  and 
the  failure  is  ascribed  to  the  perturbations  produced  by  the 
next  neighbor,  the  giant  Jupiter,  whose  powerful  attraction  is 
supposed  to  have  torn  the  ring  to  pieces,  and  thus  prevented 
its  normal  development  into  a  planet. 

Another  view  is  that  the  asteroids  may  be  fragments  of  an 
exploded  planet.  If  so,  there  must  have  been  not  one,  but 
many,  explosions,  first  of  the  original  body,  and  then  of  the 
separate  pieces ;  for  it  is  demonstrable  that  no  single  explo- 
sion could  account  for  the  present  tangle  of  orbits. 


INTRA-MERCURIAN  PLANETS  AND  THE  ZODIACAL 
LIGHT. 

264.  Intra-Mercurian   Planets.  —  It  is  very  probable,   indeed 
nearly  certain,  that  there  is  a  considerable  quantity  of  matter  circu- 
lating around  the  sun  inside  the  orbit  of  Mercury.     This  is  indicated 
by  an  otherwise  unexplained  perturbation  of  its  orbit.     It  has  been 
somewhat  persistently  supposed  that  this  intra-Mercurian  matter  is 
concentrated  into  one,  or  possibly  two,  planets  of  considerable  size, 
and  such  a  planet  has  several  times  been  reported  as  discovered,  and 
has  even  been  named  Vulcan.     The  supposed  discoveries  have  never 
been  confirmed,  however,  and  the  careful  observations  of  total  solar 
eclipses  during  the  past  ten  years  make  it  practically  certain  that 
there  is  no  "  Vulcan."     Probably,  however,  there  is  a  family  of  intra- 
Mercurian  asteroids ;  but  they  must  be  very  minute,  or  some  of  them 
would  certainly  have  been  found  either  during  eclipses  or  crossing  the 
sun's  disc ;  a  planet  as  much  as  200  miles  in  diameter  could  hardly 
have  escaped  discovery. 

265.  The  Zodiacal  Light  — This  is  a  faint  beam  of  light 
extending  from  the  sun  both  ways  along  the  ecliptic.     In  the 
evening  it  is  best  seen  in  the  early  spring,  and  in  our  latitude 
then  extends  about  90°  eastward  from  the  sun ;  in  the  tropics, 
it  is  said  that  it  can  be  followed  quite  across  the  sky.     The 


§  265]  JUPITER.  191 

region  near  the  sun  is  fairly  bright  and  even  conspicuous,  but 
the  more  distant  portions  are  extremely  faint  and  can  be 
observed  only  in  places  where  there  is  no  illumination  of  the 
air  by  artificial  lights.  Its  spectrum  is  a  simple,  continuous 
spectrum,  without  markings  of  any  kind,  so  far  as  can  be 
observed. 

We  emphasize  this,  because  of  late  it  has  been  mistakenly  reported 
that  the  bright  line  which  characterizes  the  spectrum  of  the  Aurora 
Borealis  appears  in  the  spectrum  of  the  zodiacal  light. 

The  cause  of  the  phenomenon  is  not  certainly  known.  Some 
imagine  that  the  zodiacal  light  is  only  an  extension  of  the 
solar  corona  (whatever  that  may  be),  which  is  not  perhaps 
unlikely ;  but  on  the  whole  the  more  prevalent  opinion  seems 
to  be  that  it  is  due  to  sunlight  reflected  from  myriads  of  small 
meteoric  bodies  circling  around  the  sun,  nearly  in  the  plane  of 
the  ecliptic,  thus  forming  a  thin,  flat  sheet  (something  like  one 
of  Saturn's  rings),  which  extends  far  beyond  the  orbit  of  the 
earth. 


THE  MAJOR  PLANETS.  — JUPITER. 

266.  Jupiter,  the  nearest  of  the  major  planets,  stands  next 
to  Venus  in  the  order  of  brilliance  among  the  heavenly  bodies, 
being  fully  five  or  six  times  as  bright  as  Sirius,  and  decidedly 
superior  to  Mars,  even  when  Mars  is  nearest.  It  is  not,  like 
Venus,  confined  to  the  twilight  sky,  but  at  the  time  of  opposi- 
tion dominates  the  heavens  all  night  long. 

Its  orbit  presents  no  marked  peculiarities.  The  mean  dis- 
tance of  the  planet  from  the  sun  is  a  little  more  than  five  astro- 
nomical units  (483,000000  miles),  and  the  eccentricity  of  the 
orbit  is  not  quite  -fa,  so  that  the  actual  distance  ranges  about 
21,000000  miles  each  side  of  the  mean.  At  an  average  oppo- 
sition, the  planet's  distance  from  the  earth  is  about  390,000000 
miles,  while  at  conjunction  it  is  distant  about  580,000000. 


192  DIMENSIONS,   MASS,   ETC.  [§  266 

The  inclination  of  its  orbit  to  the  ecliptic  is  only  1°  19'.  Its 
sidereal  period  is  11.86  years,  and  the  synodic  is  399  days  (a 
figure  easily  remembered),  —  a  little  more  than  a  year  and  a 
month ;  i.e.,  each  year  Jupiter  comes  to  opposition  a  month 
and  four  days  later  than  in  the  preceding  year. 


267.  Dimensions,  Mass,  Density,  etc.  —  The  planet's  appar- 
ent diameter  varies  from  50"  to  32",  according  to  its  distance 
from  the  earth.     The  disc,  however,  is  distinctly  oval,  so  that 
while  the  equatorial  diameter  is  88,200  miles,  the  polar  diam- 
eter is  only  83,000.      The  mean   diameter  (see  Art.  112)  is 
86,500  miles,  or  very  nearly  eleven  times  that  of  the  earth. 

Its  surface,  therefore,  is  119,  and  its  volume  or  bulk  1300 
times  that  of  the  earth.  It  is  by  far  the  largest  of  all  the 
planets, — larger,  in  fact,  than  all  the  rest  united. 

Its  mass  is  very  accurately  known,  both  by  means  of  its 
satellites  and  from  the  perturbations  it  produces  upon  certain 
asteroids.  It  is  j-^Vs  of  the  sun's  mass,  or  about  316  times 
that  of  the  earth. 

Comparing  this  with  its  volume,  we  find  its  mean  density  to 
be  0.24;  i.e.,  less  than  one-fourth  the  density  of  the  earth,  and 
almost  precisely  the  same  as  that  of  the  sun.  Its  surface 
gravity  is  about  2|  times  that  of  the  earth,  but  varies  nearly 
20  per  cent  between  the  equator  and  poles  of  the  planet  on 
account  of  the  rapid  rotation. 

268.  General  Telescopic  Aspect,  Albedo,  etc.  —  In  a  small 
telescope  the  planet  is  a  fine  object ;  for  a  magnifying  power 
of  only  60  makes  its  apparent  diameter,  even  when  remotest, 
equal  to  that  of  the  moon.     With  a  large  instrument  and  a 
magnifying  power  of  200  or  300,  it  is  magnificent,  the  disc 
being  covered  with  an  infinite  variety  of  detail,  interesting  in 
outline  and  rich  in  color,  changing  continually  as  the  planet 
turns   on   its   axis.      For   the   most   part  the   markings    are 


§268] 

arranged  in 
in  Fig.  55. 


TELESCOPIC    VIEWS   OF  JUPITER. 


193 


belts  "  parallel  to  the  planet's  equator,  as  shown 


The  left-hand  one  of  the  two  larger  figures  is  from  a  drawing  by 
Trouvelot  (1870),  and  the  other  from  one  by  Vogel  (1880).  The 
smaller  figure  below  represents  the  planet's  ordinary  appearance  in 
a  three-inch  telescope. 

Near  the  limb  the  light  is  less  brilliant  than  in  the  centre  of 
the  disc,  and  the  belts  there  fade  out.  The  planet  shows  no 


FIG.  55.  —  Telescopic  Views  of  Jupiter. 

perceptible  phases,  but  the  edge  which  is  turned  away  from 
the  sun  is  usually  sensibly  darker  than  the  other.  According 
to  Zollner,  the  mean  albedo  of  the  planet  is  0.62,  which  is  ex- 
tremely high,  that  of  white  paper  being  only  0.78.  The  ques- 
tion has  been  raised  whether  Jupiter  is  not  to  some  extent 


194  JUPITER.  [§268 

self-luminous,  but  there  is  DO  proof  and  little  probability  that 
such  is  the  case. 


269.  Atmosphere  and  Spectrum.  —  The  planet's  atmosphere 
must  be  very  extensive.     The  forms  which  we  see  with  the 
telescope  are  all  evidently  atmospheric.     In  fact,  the  low  mean 
density  of  the  planet  makes  it  very  doubtful  whether  there  is 
anything  solid  about  it  anywhere,  —  whether  it  is  anything 
more  than  a  ball  of  fluid  overlaid  by  cloud  and  vapor. 

The  spectrum  of  the  planet  differs  less  from  that  of  mere 
reflected  sunlight  than  might  have  been  expected,  showing 
that  the  light  is  not  obliged  to  penetrate  the  atmosphere  to 
any  great  depth  before  it  encounters  the  reflecting  envelope  of 
cloud.  There  are,  however,  certain  unexplained  dark  shadings 
in  the  red  and  orange  parts  of  the  spectrum  that  are  prob- 
ably due  to  the  planet's  atmosphere,  and  seem  to  be  identical 
in  position  with  certain  bands  which,  in  the  spectra  of  Uranus 
and  Neptune,  are  much  more  intense. 

270.  Rotation.  —  Jupiter  rotates  on  its  axis  more  swiftly 
than  any  other  of  the  planets.     Its  sidereal  day  has  a  length 
of  about  9  hours,  55  minutes,  but  the  time  can  be  given  only 
approximately,  because  different  results  are  obtained  from  dif- 
ferent spots,  according  to  their  nature  and  their  distance  from 
the  equator,  —  the  differences  amounting  to  six  or  seven  min- 
utes.    Speaking  generally,  spots  near  the  equator  indicate  a 
shorter  period  of  rotation  than  those  near  the  poles,  just  as  is 
the  case  with  the  sun. 

In  consequence  of  the  swift  rotation,  the  planet's  oblateness 
or  "  polar  compression  "  is  quite  noticeable,  —  about  -^-.  The 
plane  of  rotation  nearly  coincides  with  that  of  the  orbit,  the 
inclination  being  only  3°,  so  that  there  can  be  no  well-marked 
seasons  on  the  planet  due  to  the  causes  which  produce  our 
own  seasons. 


§  271]  PHYSICAL  CONDITION  —  SATELLITES.  195 

271,  Physical  Condition.  —  This  is  obviously  very  different 
from  that  of  the  earth  or  Mars.     No  permanent  markings  are 
found  upon  the  disc,  though  occasionally  there  are  some  which 
may  be   called  "  sub-permanent "  as,  for  instance,  the  great 
red  spot  shown  in  Fig.  55.     This  was  first  noticed  in  1878, 
became    extremely  conspicuous   for   several   years,   and  still 
(1890)  remains  visible  as  a  faded  ghost  of  itself.     Were  it  not 
that  during  the  12  years  of  its  visibility  it  has  changed  the 
length  of  its  apparent  rotation  by  about  six  seconds  (from  9 
hours,  55  minutes,  34.9  seconds  to  9  hours,  55  minutes,  40.2 
seconds),  we  might  suppose  it  permanently  attached  to  the 
planet's  surface,  and  evidence  of  a  coherent  mass  underneath. 
As  it  is,  opinion  is  divided  on  this  point ;  the  phenomenon  is 
as  puzzling  as  the  canals  of  Mars. 

Many  things  in  the  planet's  appearance  indicate  a  high 
temperature,  as,  for  instance,  the  abundance  of  clouds,  and 
the  swiftness  of  their  transformations ;  and  since  on  Jupiter 
the  solar  light  and  heat  are  only  -^  as  intense  as  here,  we  are 
forced  to  conclude  that  it  gets  very  little  of  its  heat  from  the 
sun,  but  is  probably  hot  on  its  own  account,  and  for  the  same 
reason  that  the  sun  is  hot ;  viz.,  as  the  result  of  a  process  of 
condensation.  In  short,  it  appears  very  probable  that  the 
planet  is  a  sort  of  semi-sun,  —  hot,  though  not  so  hot  as  to  be 
sensibly  self-luminous. 

272.  Satellites. — Jupiter  has  a  retinue  of  four  large  satel- 
lites,—  the   first  heavenly  bodies    ever   discovered.      Galileo 
found  them  in  January,  1610,  within  a  very  few  weeks  after 
his  invention  of  the  telescope. 

They  are  now  usually  known  as  the  first,  second,  etc.,  in  the 
order  of  their  distance  from  the  planet.  The  distances  range 
from  262,000  to  1,169,000  miles,  being  respectively  6,  9,  15, 
and  26  radii  of  the  planet  (nearly).  Their  sidereal  periods 
range  from  42  hours  to  16f  days.  Their  orbits  are  sensibly 
circular,  and  lie  very  nearly  in  the  plane  of  the  equator.  The 


196  SATELLITES   OF  JUPITER.  [§272 

third  satellite  is  much  the  largest,  having  a  diameter  of  about 
3600  miles,  while  the  others  are  between  2000  and  3000. 

For  some  reason,  the  fourth  satellite  is  a  very  dark-complexioned 
body,  so  that  when  it  crosses  the  planet's  disc  it  looks  like  a  black 
spot  hardly  distinguishable  from  its  own  shadow :  the  others,  under 
similar  circumstances,  appear  bright,  dark,  or  invisible,  according 
to  the  brightness  of  the  part  of  the  planet  which  happens  to  form 
the  background.  In  Fig.  55  a  satellite  and  its  shadow  are  visible 
together  near  the  eastern  limb  of  the  planet.  In  the  case  of  the 
fourth  satellite,  a  certain  regularity  in  its  changes  of  brightness  sug- 
gests that  it  probably  follows  the  example  of  our  moon  in  always 
keeping  the  same  face  towards  the  planet. 

273.  Eclipses  and  Transits.  —  The  orbits  of  the  satellites  are 
so  nearly  in  the  plane  of  the  planet's  orbit  that  with  the  ex- 
ception of  the  fourth,  which  sometimes  escapes,  they  are 
eclipsed  at  every  revolution.  When  the  planet  is  either  at 
opposition  or  conjunction,  the  shadow,  of  course,  is  directly 
behind  it,  and  we  cannot  see  the  eclipse  at  all.  At  other  times 
we  ordinarily  see  only  the  beginning  or  the  end  ;  but  when  the 
planet  is  very  near  quadrature  the  shadow  projects  so  far  to 
one  side  that  the  whole  eclipse  of  every  satellite,  except  the 
first,  takes  place  clear  of  the  disc,  and  both  the  disappearance 
and  reappearance  can  be  seen. 

Two  important  uses  have  been  made  of  these  eclipses  :  they 
have  been  employed  for  the  determination  of  longitude,  and 
they  furnish  the  means  of  ascertaining  the  time  required  by  light 
to  traverse  the  space  between  the  earth  and  the  sun.  (See  Appen- 
dix, Arts.  431-434.) 


SATURN. 

X 
274,   This  is  the  most  remote  of  the  planets  known  to  the 

ancients.     It  appears  as  a  star  of  the  first  magnitude  (out- 
shining all  of  them,  indeed,  except  Sirius),  with  a  steady, 


§  274]  SATURN.  197 

yellowish  light,  not  varying  much  in  appearance  from  month 
to  month,  though  in  the  course  of  15  years  it  alternately  gains 
and  loses  nearly  50  per  cent  of  its  brightness  with  the  chang- 
ing phases  of  its  rings ;  for  it  is  unique  among  the  heavenly 
bodies,  a  great  globe  attended  by  eight  satellites  and  sur- 
rounded by  a  system  of  rings,  which  has  no  counterpart  else- 
where in  the  universe  so  far  as  known. 

Its  mean  distance  from  the  sun  is  about  9|-  astronomical 
units,  or  886,000000  miles;  but  the  distance  varies  over 
100,000000  miles  on  account  of  the  considerable  eccentricity  of 
the  orbit  (0.056).  Its  least  distance  from  the  earth  is  about 
774,000000  miles,  the  greatest,  about  1028,000000.  The  incli- 
nation of  the  orbit  to  the  ecliptic  is  2^-°.  The  sidereal  period 
is  about  29^  years,  the  synodic  period  being  378  days,  or  a  year 
and  a  fortnight  nearly. 

275.  Dimensions,  Mass,  etc. — The  apparent  mean  diameter 
of  the  planet  varies  according  to  the  distance  from  14"  to  20". 
The  planet  is  more  flattened  at  the  poles  than  any  other 
(nearly  y1-^),  so  that  while  the  equatorial  diameter  is  about 
75,000  miles,  the  polar  is  pnly  68,000 :  the  mean  diameter 
(Art.  112)  being  not  quite  •  73,000,  —  a  little  more  than  nine 
times  that  of  the  earth.  Its  surface  is  about  84  times  that  of 
the  earth,  and  its  volume  770  times.  Its  mass  is  found  (by 
means  of  its  satellites)  to  be  95  times  that  of  the  earth,  so 
that  its  mean  density  comes  out  only  one-eighth  that  of  the 
earth,  —  actually  less  than  that  of  water  !  It  is  by  far  the  least 
dense  of  all  the  planetary  family. 

Its  mean  superficial  gravity  is  about  1.2  times  as  great  as 
gravity  upon  the  earth,  varying,  however,  nearly  25  per  cent 
between  the  equator  and  the  pole,  so  that  at  the  planet's 
equator  it  is  practically  the  same  as  upon  the  earth.  It 
rotates  on  its  axis  in  about  10  hours,  14  minutes,  but  there 
is  reason  to  suspect  that  different  spots  would  give  results 
varying  with  their  latitude,  as  in  the  case  of  Jupiter. 


198 


SATURN. 


[§275 


FIG.  56.  —  Saturn  and  his  Rings. 


SURFACE,    ALBEDO,    SPECTRUM.  199 

The  equator  of  the  planet  is  inclined  about  27°  to  the  plane 
of  its  orbit — about  28°  to  the  ecliptic. 


276.  Surface,  Albedo,  Spectrum.  —  The  disc  of  the  planet, 
like  that  of  Jupiter,  is  shaded  at  the  edge,  and  like  Jupiter  it 
shows  a  number  of  belts  arranged  parallel  to  the  equator. 
The  equatorial  belt  is  very  bright,  and  is  often  of  a  delicate 
pinkish  tinge.     The  belts  in  higher  latitudes  are  comparatively 
faint  and  narrow,  while  just  at  the  pole  there  is  usually  a  cap 
of  olive  green  (see  Fig.  56). 

Zollner  makes  the  mean  albedo  of  the  planet  0.52,  about  the 
same  as  that  of  Venus. 

The  planet's  spectrum  is  substantially  like  that  of  Jupiter, 
but  the  dark  bands  are  more  pronounced.  These  bands,  how- 
ever, do  not  appear  in  the  spectrum  of  the  ring,  which  prob- 
ably has  very  little  atmosphere.  As  to  its  physical  condition 
and  constitution,  the  planet  is  probably  much  like  Jupiter, 
though  it  does  not  seem  to  be  "  boiling  "  quite  so  vigorously. 

277.  The  Rings.  —  The  most  remarkable  peculiarity  of  the 
planet  is  its  ring  system.     The  globe  is  surrounded  by  three 
thin,  flat,  concentric  rings,  like  circular  discs  of  paper  pierced 
through  the  centre.     They  are  generally  referred  to  as  A,  B, 
and  C,  A  being  the  exterior  one. 

Galileo  half  discovered  them  in  1610 ;  i.e.,  he  saw  with  his  little 
telescope  two  appendages,  one  on  each  side  of  the  planet ;  but  he  could 
make  nothing  of  them,  and  after  a  while  he  lost  them.  The  problem 
remained  unsolved  for  nearly  fifty  years,  until  Huyghens  explained 
the  mystery  in  1655.  Twenty  years  later  D.  Cassini  discovered  that 
the  ring  is  double ;  i.e.,  composed  of  two  concentric  rings,  with  a  dark- 
line  of  separation  between  them ;  and  in  1850,  Bond  of  Cambridge, 
U.S.,  discovered  the  third  "dusky"  or  "gauze"  ring  between  the 
principal  ring  and  the  planet.  (It  was  discovered  a  fortnight  later, 
independently,  by  Dawes,  in  England.) 


200  SATURN'S  RINGS.  [§277 

The  outer  ring,  A,  has  a  diameter  of  about  168,000  miles, 
and  a  width  of  about  10,000.  Cassini's  division  is  about  1000 
miles  wide;  the  ring  B,  which  is  much  the  broadest  of  the 
three,  is  about  17,000.  The  semi-transparent  ring,  (7,  has  a 
width  of  about  9000  miles,  leaving  a  clear  space  of  from  9000 
to  10,000  miles  in  width  between  the  planet's  equator  and  its 
inner  edge.  The  thickness  of  the  rings  is  extremely  small,  — 
probably  not  over  100  miles,  as  proved  by  the  appearance 
presented,  when  once  in  15  years  we  view  them  edgewise. 

278.  Phases  of  the  Rings.  —  The  plane  of  the  rings  coin- 
cides with  the  plane  of  the  planet's  equator,  and  is  inclined 


FIG.  57.  —  The  Phases  of  Saturn's  Rings. 

about  28°  to  the  ecliptic.  It,  of  course,  remains  parallel 
to  itself  at  all  times.  Twice  in  a  revolution  of  the  planet, 
therefore,  this  plane  sweeps  across  the  orbit  of  the  earth  (too 
small  to  be  shown  in  the  figure  —  Fig.  57),  occupying  nearly  a 
year  in  so  doing ;  and  whenever  the  plane  passes  between  the 
earth  and  the  sun  the  dark  side  of  the  ring  is  towards  us,  and 
the  edge  alone  is  visible,  as  when  the  planet  is  at  1  or  2; 
when  it  is  at  the  intermediate  points  3  and  4  the  rings  present 
their  widest  opening. 


§  278]  SATELLITES.  .       201 

When  the  ring  is  exactly  edgewise  towards  us  only  the  largest  tele- 
scopes can  see  it,  like  a  fine  needle  of  light  piercing  the  planet's  ball, 
as  in  the  uppermost  engraving  of  Fig.  56.  It  becomes  obvious  at 
such  times  that  the  thickness  of  the  rings  is  not  uniform,  since  con- 
siderable irregularities  appear  upon  the  line  of  light  at  different 
points.  The  last  period  of  disappearance  was  in  1877-78 ;  the  next 
will  be  in  1892-93. 

279.  Structure  of  the  Rings.  —  It  is  now  universally  ad- 
mitted that  they  are  not  continuous  sheets,  either  solid  or 
liquid,  but  mere  swarms  of  separate  particles,  each  particle  pur- 
suing its  own  independent  orbit  around  the  planet,  though  all 
moving  nearly  in  a  common  plane. 

The  idea  was  first  suggested  by  J.  Cassini  in  1715,  but  was  lost 
sight  of  until  again  suggested  by  Bond  in  connection  with  his  dis- 
covery of  the  semi-transparent  or  dusky  ring ;  it  has  finally  been  estab- 
lished by  the  researches  of  Pierce,  Maxwell,  and  others,  who  have 
shown  that  no  solid  or  liquid  sheet  could  maintain  itself  for  any 
length  of  time  under  the  circumstances. 

The  recent  investigations  of  H.  Struve  show  that  the  aggre- 
gate mass  of  the  rings  is  extremely  small,  —  so  small  that 
they  exert  no  sensible  influence  on  the  motion  of  the  satellites. 

It  is  a  question  not  yet  settled  whether  the  rings  constitute 
a  permanently  stable  system,  or  are  liable  ultimately  to  be 
broken  up. 

280.  Satellites.  —  Saturn  has  eight  of  these  attendants,  the 
largest  of  which  was  discovered  by  Huyghens  in  1655.     It 
looks  like  a  star  of  the  ninth  magnitude,  and  is  easily  seen 
with  a  three-inch  telescope.     The  smallest  one,  the  seventh  in 
order  of  distance  from  the  planet,  was  discovered  by  Bond,  at 
Cambridge  (U.S.)  in  1848. 

Since  the  order  of  discovery  does  not  agree  with  that  of  distance,  it 
has  been  found  convenient  to  designate  them  by  the  names  assigned 


202       -  URANUS.  [§280 

by  Sir  John  Herschel,  as  follows,  beginning  with  the  most  remote 
viz. : — 

lapetus  (Hyperion),  Titan,  Rhea,  Dione,  Tethys; 

Enceladus,  Mimas. 

The  range  of  the  system  is  enormous.  lapetus  has  a  distance  of 
2,225,000  miles,  with  a  period  of  79  days,  nearly  as  long  as  that  of 
Mercury.  On  the  western  side  of  the  planet,  this  satellite  is  always 
much  brighter  than  upon  the  eastern,  showing  that,  like  our  own 
moon,  it  keeps  the  same  face  towards  its  primary. 

Titan,  as  its  name  suggests,  is  by  far  the  largest.  Its  distance  is 
about  770,000  miles,  and  its  period  a  little  less  than  16  days.  It  is 
probably  3000  or  4000  miles  in  diameter,  and,  according  to  Stone,  its 
mass  is  ^^7  of  Saturn's,  or  about  double  that  of  our  moon.  The  orbit 
of  lapetus  is  inclined  nearly  10°  to  the  plane  of  the  rings,  but  all  of 
the  other  satellites  move  almost  exactly  in  their  plane,  and  all  the  five 
inner  ones  in  orbits  nearly  circular. 

URANUS. 

281.  Uranus  (not  U-ra'nus)  was  the  first  planet  ever  "dis- 
covered," and  the  discovery  created  great  excitement  and 
brought  the  highest  honors  to  the  astronomer.  It  was  found 
accidentally  by  the  elder  Herschel  on  March  13,  1781,  while 
"  sweeping  "  for  interesting  objects  with  a  seven-inch  reflector 
of  his  own  construction.  He  recognized  it  at  once  by  its  disc 
as  something  different  from  a  star,  but  supposed  it  to  be  a 
peculiar  sort  of  a  comet,  and  its  planetary  character  was  not 
demonstrated  until  nearly  a  year  had  passed.  It  is  easily 
visible  to  a  good  eye  as  a  star  of  the  sixth  magnitude. 

Its  mean  distance  from  the  sun  is  about  19  times  that  of  the 
earth,  or  about  1800,000000  miles,  and  the  eccentricity  of  its 
orbit  is  about  the  same  as  that  of  Jupiter's.  The  inclination 
of  the  orbit  to  the  ecliptic  is  very  slight  —  only  46'.  The  side- 
real period  is  84  years,  and  the  synodic,  369^  days. 

In  the  telescope  it  shows  a  greenish  disc  about  4"  in  diam- 
eter, which  corresponds  to  a  real  diameter  of  about  32,000 


§  2811  SATELLITES   OF   URANUS.  203 

miles.  This  makes  its  bulk  about  66  times  that  of  the  earth. 
The  planet's  mass  is  found  from  its  satellites  to  be  about  14.6 
times  that  of  the  earth ;  its  density,  therefore,  is  0.22  —  about 
the  same  as  that  of  Jupiter  and  the  sun. 

The  albedo  of  the  planet,  according  to  Zollner,  is  very  high, 
0.64,  —  even  a  little  above  that  of  Jupiter.  The  spectrum 
exhibits  intense  dark  bands  in  the  red,  due  to  some  unidenti- 
fied substance  in  the  planet's  atmosphere.  These  bands  explain 
the  marked  greenish  tint  of  the  planet's  light.  The  atmos- 
phere is  probably  dense. 

The  disc  is  obviously  oval,  with  an  ellipticity  of  about  T\. 
There  are  no  clear  markings  upon  it,  but  there  seem  to  be 
faint  traces  of  something  like  belts.  No  spots  are  visible  from 
which  to  determine  the  planet's  diurnal  rotation. 

282.  Satellites.  —  The  planet  has  four  satellites,  —  Ariel, 
Umbriel,  Titania,  and  Oberon,  —  Ariel  being  the  nearest  to  the 
planet. 

The  two  brightest,  Oberon  and  Titania,  were  discovered  by  Sir 
William  Herschel  a  few  years  after  his  discovery  of  the  planet; 
Ariel  and  Umbriel,  by  Lassell,  in  1851. 

They  are  among  the  smallest  bodies  in  the  solar  system,  and 
the  most  difficult  to  see. 

Their  orbits  are  sensibly  circular,  and  all  lie  in  one  plane, 
which  ought  to  be,  and  probably  is,  coincident  with  the  plane 
of  the  planet's  equator. 

They  are  very  close  packed  also,  Oberon  having  a  distance  of  only 
375,000  miles,  and  a  period  of  13  days,  11  hours,  while  Ariel  has  a 
period  of  2  days,  12  hours,  at  a  distance  of  120,000  miles.  Titania, 
the  largest  and  brightest  of  them,  has  a  distance  of  280,000  miles, 
somewhat  greater  than  that  of  the  moon  from  the  earth,  with  a  period 
of  8  days,  17  hours. 

The  most  remarkable  thing  about  this  system  remains  to  be 
mentioned.  The  plane  of  their  orbits  is  inclined  82°.2,  or 


204  DISCOVERY  OF  NEPTUNE.  [§  282 

almost  perpendicularly,  to  the  plane  of  the  ecliptic  j  and  in 
that  plane  they  revolve  backwards. 


NEPTUNE. 

283.  Discovery.  —  The  discovery  of  this  planet  is  reckoned 
the  greatest  triumph  of  mathematical  astronomy.  Uranus 
failed  to  move  precisely  in  the  path  computed  for  it,  and  was 
misguided  by  some  unknown  influence  to  an  extent  which 
could  almost  be  seen  with  the  naked  eye.  The  difference 
between  the  actual  and  computed  places  in  1845  was  the  "  in- 
tolerable quantity  "  of  nearly  two  minutes  of  arc. 

This  is  a  little  more  than  half  the  distance  between  the  two  prin- 
cipal components  of  the  double-double  star,  Epsilon  Lyrae,  the  north- 
ern one  of  the  two  little  stars  which  form  the  small  equilateral  triangle 
with  Vega  (Arts.  67  and  375).  A  very  sharp  eye  detects  the  duplicity 
of  Epsilon  without  the  aid  of  a  telescope. 

One  might  think  that  such  a  minute  discrepancy  between 
observation  and  theory  was  hardly  worth  minding,  and  that 
to  consider  it  "  intolerable  "  was  putting  the  case  very  strongly. 
But  just  these  minute  discrepancies  supplied  the  data  which 
were  found  sufficient  for  calculating  the  position  of  a  great 
unknown  world,  and  bringing  it  to  light.  As  the  result  of  a 
most  skilful  and  laborious  investigation,  Leverrier  (born  1811, 
died  1877)  wrote  to  Galle  in  substance :  — 

"Direct  your  telescope  to  a  point  on  the  ecliptic  in  the  constellation  of 
Aquarius,  in  longitude  326°,  and  you  will  find  within  a  degree  of  that 
place  a  new  planet,  looking  like  a  star  of  about  the  ninth  magnitude,  and 
having  a  perceptible  disc." 

The  planet  was  found  at  Berlin  on  the  night  of  Sept.  23, 
1846,  in  exact  accordance  with  this  prediction,  within  half  an 
hour  after  the  astronomers  began  looking  for  it,  and  within 
52'  of  the  precise  point  that  Leverrier  had  indicated. 


§  283]  THE  PLANET  AND  ITS   ORBIT.  205 

We  cannot  here  take  the  space  for  a  historical  statement,  further 
than  to  say  that  the  English  Adams  (now  Professor  of  Astronomy  at 
Cambridge,  England)  fairly  divides  with  Leverrier  the  credit  for  the 
mathematical  discovery  of  the  planet,  having  solved  the  problem  and 
deduced  the  planet's  approximate  place  even  earlier  than  his  competi- 
tor. The  planet  was  being  searched  for  in  England  at  the  time  it  was 
found  in  Germany.  In  fact,  it  had  already  been  observed,  and  the 
discovery  would  necessarily  have  followed  in  a  few  weeks,  upon  the 
reduction  of  the  observations. 

284.  Error  of  the  Computed  Orbit.  —  Both  Adams  and  Lever- 
rier, besides  calculating  the  planet's  position  in  the  sky,  had  deduced 
elements  of  its  orbit  and  a  value  for  its  mass,  which  turned  out  to  be 
seriously  wrong,  and  certain  high  authorities  have  therefore  character- 
ized the  discovery  as  a  "  happy  accident."     This  is  not  so,  however. 
While  the  data  and  methods  employed  were  not  sufficient  to  deter- 
mine the  planet's  orbit  with  accuracy,  they  were  adequate  to  ascertain 
the  planet's  direction  from  the  earth.     The  computers  informed  the 
observers  where  to  point  their  telescopes,  and  this  was  all  that  was  neces- 
sary for  finding  the  planet. 

285.  The  Planet  and  its  Orbit.  —  The  planet's  mean  distance 
from  the  sun  is  a  little  more  than  2800,000000  miles  (800,- 
000000  miles  nearer  the  sun  than  it  should  be  according  to 
Bode's  Law).     The  orbit  is  very  nearly  circular,  its  eccentricity 
being  only  0.009.     The  inclination  of* the  orbit  is  about  1|°. 
The  period  of  the  planet  is  about  164  years  (instead  of  217,  as 
as   it   should  have  been  according  to   Leverrier's   computed 
orbit),  and  the  orbital  velocity  is  about  3^  miles  per  second. 

Neptune  appears  in  the  telescope  as  a  small  star  of  between 
the  eighth  and  ninth  magnitudes,  absolutely  invisible  to  the 
naked  eye,  though  easily  seen  with  a  good  opera-glass.  Like 
Uranus,  it  shows  a  greenish  disc,  having  an  apparent  diameter 
of  about  2 ".6.  The  real  diameter  of  the  planet  is  about  35,000 
miles,  and  the  volume  a  little  more  than  90  times  that  of  the 
earth. 

Its  mass,  as  determined  by  means  of  its  satellite,  is  about 
18  times  that  of  the  earth,  and  its  density  0.20. 


206  NEPTUNE'S  SATELLITE.  [§285 

The  planet's  albedo,  according  to  Zollner,  is  0.46,  a  trifle 
less  than  that  of  Saturn  and  Venus. 

There  are  no  visible  markings  upon  its  surface,  and  nothing 
certain  is  known  as  to  its  rotation. 

The  spectrum  of  the  planet  appears  to  be  like  that  of 
Uranus,  but  of  course  is  rather  faint. 

It  will  be  noticed  that  Uranus  and  Neptune  form  a  "  pair  of  twins," 
very  much  as  the  earth  and  Venus  do,  being  almost  alike  in  magni- 
tude, density,  and  many  other  characteristics. 

286.  Satellite. — Neptune  has  one  satellite,  discovered  by 
Lassell  within   a   month   after   the   discovery  of  the  planet 
itself.     Its   distance  is  about  223,000   miles,  and  its   period 
5d  21h.     Its  orbit  is  inclined  to  the  ecliptic  at  an  angle  of  34° 
48',  and  it  moves  backward  in  it  from  east  to  west,  like  the 
satellites  of  Uranus.     From  its  brightness,  as  compared  with 
that  of  Neptune  itself,  its  diameter  is  estimated  as  about  the 
same  as  that  of  our  own  moon. 

287.  The  Solar  System  as  seen  from  Neptune. — At  Nep- 
tune's distance  the  sun  itself  has  an  apparent   diameter  of 
only  a  little  more  thai\  one  minute  of  arc,  —  about  the  diam- 
eter of  Venus  when  nearest  us,  and  too  small  to  be  seen  as  a 
disc  by  the  naked  eye,  if  there  are  eyes  on  Neptune.     The 
solar  light  and  heat  are  there  only  ^  of  what  we  get  at  the 
earth. 

Still,  we  must  not  imagine  that  the  Neptunian  sunlight  is 
feeble  as  compared  with  starlight,  or  even  moonlight.  Even 
at  the  distance  of  Neptune  the  sun  gives  a  light  nearly  equal 
to  700  full  moons.  This  is  about  80  times  the  light  of  a 
standard  candle  at  one  metre's  distance,  and  is  abundant  for 
all  visual  purposes.  In  fact,  as  seen  from  Neptune,  the  sun 
would  look  very  like  a  large  electric  arc  lamp,  at  a  distance  of 
a  few  yards. 


§  288]  ULTRA-NEPTUNIAN  PLANETS,   ETC.  207 

288.  Ultra-Neptunian  Planets.  —  Perhaps  the  breaking  down  of 
Bode's  Law  at  Neptune  may  be  regarded  as  an  indication  that  the 
solar  system  terminates  there,  and  that  there  is  no  remoter  planet ; 
but  of  course  it  does  not  make  it  certain.  If  such  a  planet  exists,  it 
is  sure  to  be  found  sooner  or  later,  either  by  means  of  the  disturbances 
it  produces  in  the  motion  of  Uranus  and  Neptune,  or  else  by  the 
methods  of  the  asteroid  hunters,  although  its  slow  motion  will  render 
its  discovery  in  that  way  difficult.  Quite  possibly  such  a  discovery 
may  come  within  a  few  years  as  a  result  of  the  photographic  star- 
charting  operations  now  in  progress. 

288*.  Stability  of  the  Solar  System.  —  It  is  an  interesting  and 
important  question,  once  long  and  warmly  discussed,  whether  the  so- 
called  "perturbations"  which  result  from  the  mutual  attractions  of 
the  planets  can  ever  seriously  derange  the  system.  It  is  now  nearly 
a  century  since  Laplace  and  Lagrange  first  demonstrated  that  they 
cannot.  The  system  is  stable  in  itself,  all  the  planetary  disturbances 
due  to  gravitation  being  either  of  such  a  character,  or  so  limited  in 
extent,  that  they  can  never  do  any  harm. 

It  does  not  follow,  however,  that  because  the  mutual  attractions  of 
the  planets  are  thus  harmless,  there  may  not  be  other  causes  which 
would  act  disastrously.  Many  such  are  conceivable,  —  such,  for  in- 
stance, as  the  retardation  of  the  speed  of  the  planets  which  would  be 
caused  by  the  presence  of  a  resisting  medium  in  space,  or  by  the  en- 
counter of  the  system  with  a  sufficiently  dense  and  extended  cloud  of 
meteors. 

But  so  far  as  we  can  now  judge,  the  ultimate  cooling  of  the  sun 
(Art.  193)  is  likely  to  extinguish  life  upon  the  planets  long  before  the 
mechanical  destruction  of  the  system  can  occur  from  any  such  exter- 
nal causes. 


208  COMETS.  [§  289 


CHAPTER   X. 

COMETS   AND    METEOKS. 

THE  NUMBER,  DESIGNATION,  AND  ORBITS  OF  COMETS. — 
THEIR  CONSTITUENT  PARTS  AND  APPEARANCE.  —  THEIR 
SPECTRA  AND  PHYSICAL  CONSTITUTION.  —  THEIR  PROB- 
ABLE ORIGIN.  —  REMARKABLE  COMETS.  —  AEROLITES, 
THEIR  FALL  AND  CHARACTERISTICS.  —  SHOOTING  STARS, 
METEORIC  SHOWERS.  —  CONNECTION  BETWEEN  COMETS 
AND  METEORS. 

289.  Comets  —  their  Appearance  and  Number.  —  The  word 
"  comet"  (derived  from  the  Greek  kom£)  means  a  "hairy  star." 
The  appearance  is  that  of  a  rounded  cloud  of  luminous  fog 
with  a  star  shining  through  it,  often  accompanied  by  a  long 
fan-shaped  train  or  "  tail  "  of  hazy  light.  They  present  them- 
selves from  time  to  time  in  the  heavens,  mostly  when  unex- 
pected, move  across  the  constellations  in  a  path  longer  or 
shorter  according  to  circumstances,  and  remain  visible  for  some 
weeks  or  months,  until  they  fade  out  and  vanish  in  the  dis- 
tance. The  large  ones  are  magnificent  objects,  sometimes  as 
bright  as  Venus,  and  visible  by  day ;  with  a  head  as  large  as 
the  moon,  and  having  a  train  which  extends  from  the  horizon 
to  the  zenith,  and  is  really  long  enough  to  reach  from  the  earth 
to  the  sun.  Such  comets  are  rare,  however.  The  majority  are 
faint  wisps  of  light,  visible  only  with  the  telescope.  Fig.  58 
is  a  representation  of  Donati's  comet  of  1858,  which  was  one  of 
the  finest  ever  seen. 


289] 


COMETS. 


209 


Fi0.  58.  —Naked-eye  View  of  Donati's  Comet,  Oct.  4, 1858.     (Bond.) 

In  ancient  times,  comets  were  always  regarded  with  terror,  as  at 
least  presaging  evil,  if  not  actively  malignant,  and  the  notion  still 
survives  in  certain  quarters,  though  the  most  careful  research  goes  to 


210  DESIGNATION  OF   COMETS,  [§289 

prove  that  they  really  do  not  exert  upon  the  earth  the  slightest  per- 
ceptible influence  of  any  kind. 

Thus  far  our  lists  contain  about  650,  about  400  of  which 
were  observed  before  the  invention  of  the  telescope,  and  there- 
fore must  have  been  fairly  bright.  Of  the  250  observed  since 
then,  only  a  small  proportion  have  been  conspicuous  to  the 
naked  eye,  perhaps  one  in  five.  The  total  number  that  visit 
the  solar  system  must  be  enormous ;  for  there  is  seldom  a  time 
when  one  at  least  is  not  in  sight,  and  even  with  the  telescope 
we  see  only  the  few  which  come  near  the  earth  and  are  favor- 
ably situated  for  observation. 

290.  Designation  of  Comets.  —  A  remarkable  comet  gener- 
ally bears  the  name  of  its  discoverer  or  of  some  one  who  has 
"acquired  its  ownership,"  so  to  speak,  by  some   important 
research  concerning  it.     Thus  we  have  Halley's,  Encke's,  and 
Donati's   comets.     The  ordinary  telescopic  comets  are  desig- 
nated only  by  the  year  of  discovery  with  a  letter  indicating 
the  order  of  discovery  in  that  year,  as  comet  "  1890  a  " ;  or  still 
again,  with  the  year  and  a  Eoman  numeral  denoting  the  order 
of  perihelion  passage,  as  1890  I,  the  latter  method  being  the 
most  used.     In  some  cases  a  comet  bears  a  double  name,  as 
the  Lexell-Brooks  comet  (1889  V),  which  was  investigated  by 
Lexell  in  1770,  and  discovered  by  Brooks  on  its  recent  return  in 
1889. 

291.  Duration  of    Visibility  and  Brightness. — The  great 
comet  of  1811  was  observed  for  seventeen  months,  and  the 
little  comet,  known  as  1889  I,  for  more  than  two  years,  the 
longest  period  of  visibility  on  record.      On  the  other  hand, 
the  whole  appearance  sometimes  lasts  only  a  week  or  two.    The 
average  is  probably  not  far  from  three  months. 

As  to  brightness,  comets  differ  widely.  About  one  in  five 
reaches  the  naked-eye  limit,  and  a  very  few,  say  four  or  five  in 


§291]  THEIR    ORBITS.  211 

a  century,  are  bright  enough  to  be  seen  in  the  day-time.     The 
great  comet  of  1882  was  the  last  one  so  visible. 

292.  Their  Orbits.  —  A  large  majority  of  the  comets  move 
in  orbits  that  are  sensibly  parabolas  (see  Appendix,  Arts.  439- 
440).     A  comet  moving  in  such  an  orbit  approaches  the  sun 
from  an  enormous  distance,  far  beyond  the  limits  of  the  solar 
system,  sweeps  once  around  the  sun,  and  goes  off,  never  to 
come  back.   The  parabola  does  not  return  into  itself  and  form  a 
closed  curve,  like  the  circle  and  ellipse,  but  recedes  to  infinity. 
Of  the  270  orbits  that  have  been  computed,  more  than  200 
appear  to  be  of  this  kind.     About  60  orbits  are  more  or  less 
distinctly  elliptical,  and  about  half  a  dozen  are  perhaps  hyper- 
bolas (see  Appendix,  Art.  440) ;  but  the  hyperbolas  differ  so 
slightly  from  parabolas  that  the  hyperbolic  character  is  not 
really  certain  in  a  single  case. 

Comets  which  have  elliptical  orbits  of  course  return  at  regu- 
lar intervals.  Of  the  60  elliptical  orbits,  there  are  about  a 
dozen  to  which  computation  assigns  periods  near  to  or  exceed- 
ing 1000  years.  These  orbits  approach  parabolas  so  closely 
that  their  real  character  is  still  rather  doubtful.  About  50 
comets,  however,  have  orbits  which  are  distinctly  and  certainly 
elliptical,  and  28  have  periods  of  less  than  one  hundred  years. 
Fourteen  of  these  28  have  been  actually  observed  at  two  or 
more  returns  at  perihelion.  As  to  the  rest  of  them,  some  are 
now  due  within  a  few  years,  and  some  have  probably  been  lost 
to  observation,  either  like  Biela's  comet  (Art.  312),  or  by  hav- 
ing their  orbits  transformed  by  perturbations. 

293.  The  first  comet  ascertained  to  move  in  an  elliptical  orbit  was 
that  known  as  Halley's,  with  a  period  of  about  seventy-six  years,  its 
periodicity  having  been  discovered  by  Halley  in  1681.     It  has  since 
been  observed  in  1759  and  1835,  and  is  expected  again  about  1911. 
The  second  of  the  periodic  comets   (in  the  order  of  discovery)  is 
Encke's,  with  the  shortest  period  known,  —  only  three  and  one-half 
years.     Its  periodicity  was  discovered  in  1819,  though  the  comet  itself 


212 


COMET   GROUPS. 


[§293 


had  been  observed  several  times  before.  Fig.  59  shows  the  orbits  of  a 
number  of  short  period  comets  (it  would  cause  confusion  to  insert 
more  of  them),  and  also  a  part  of  the  orbit  of  Halley's  comet.  These 
comets  all  have  periods  ranging  from  three  and  one-half  to  eight  years, 
and  it  will  be  noticed  that  they  all  pass  very  near  to  the  orbit  of 
Jupiter.  Moreover,  each  comet's  orbit  crosses  that  of  Jupiter  near 
one  of  its  nodes,  the  node  being  marked  by  a  short  cross-line  on  the 


FIG.  59.  —  Orbits  of  Short-period  Comets. 

comet's  orbit.  The  fact  is  very  significant,  showing  that  these  comets 
at  times  come  very  near  to  Jupiter,  and  it  points  to  an  almost  certain 
connection  between  that  planet  and  these  bodies. 


294.  Comet  Groups.  —  There  are  several  instances  in  which  a 
number  of  comets,  certainly  distinct,  chase  each  other  along  almost 
exactly  the  same  path,  at  an  interval  usually  of  a  few  months  or  years, 
though  they  sometimes  appear  simultaneously.  The  most  remarkable 
of  these  "comet  groups  "  is  that  composed  of  the  great  comets  of  1668, 
1843,  1880,  1882,  and  1887.  It  is  of  course  nearly  certain  that  the 
comets  of  such  a  "  group  "  have  a  common  origin. 


§295]  PERIHELION  DISTANCE.  213 

295.  Perihelion  Distance,  etc. — Eight  of  -the  270  cometary 
orbits,  thus  far  determined,  approach  the  sun  within  less  than 
6,000000  miles,  and  four  have  a  perihelion  distance  exceeding 
200,000000.     A  single  comet  (that  of  1729)  had  a  perihelion 
distance  of  more  than  four  '  astronomical  units/  or  375,000000 
miles.     It  must  have  been  an  enormous  one,  to  be  visible  at 
all  under  the  circumstances.      There  may,  of  course,  be  any 
number   of    comets    with   still    greater  perihelion  distances, 
because  as  a  rule  we  are  only  able  to  see  such  as  come  reason- 
ably near  the  earth,  and  this  is  probably  only  a  small  percent- 
age of  the  total  number  that  visit  the  sun. 

The  inclinations  of  cometary  orbits  range  all  the  way  from 
zero  to  90°.  As  regards  the  direction  of  motion,  all  the  ellip- 
tical comets  having  periods  of  less  than  100  years  move  direct, 
i.e.,  from  west  to  east,  except  Halley's  comet  and  TempePs 
comet  of  1886.  Other  comets  show  no  decided  preponderance 
either  way. 

296.  Parabolic  Comets  are  Visitors.  —  The  fact  that  the 
orbits  of  most  comets  are  sensibly  parabolic,  and  that  their 
planes    have   no   evident  relation  to  the  ecliptic,   indicates 
(though  it  does  not  absolutely  prove)  that  these  bodies  do  not 
in  any  proper  sense  belong  to  the  solar  system.     They  are  only 
visitors.     Such  comets  come  to  us  precisely  as  if  they  simply 
dropped  towards  the  sun  from  an  enormous  distance  among 
the  stars ;  and  they  leave  the  system  with  a  velocity  which, 
if  no  force  but  the   sun's   attraction   acts   upon  them,  will 
carry  them  away  to  an  infinite  distance,  or  until  they  encoun- 
ter the  attraction  of  some  other  sun.     Their  motions  are  just 
what  might  be  expected  of  ponderable  masses  moving  among 
the  stars  under  the  law  of  gravitation. 

297.  Origin  of  Periodic  Comets. — But  while  the  parabolic 
comets  are  thus  unquestionably  strangers  and  visitors,  there  is 
a  question  as  to  the  periodic  comets,  which  move  in  elliptical 


214  THE   CAPTURE   THEORY.  [§  297 

orbits.  Are  we  to  regard  them  as  native  citizens,  or  only  as 
naturalized  foreigners,  so  to  speak  ?  It  is  evident  that,  some- 
how or  other,  many  of  them  stand  in  peculiar  relations  to 
Jupiter,  Saturn,  and  other  planets,  as  already  indicated  in  Art. 
293.  All  short  period  comets  (those  which  have  periods 
ranging  from  three  to  eight  years)  pass  very  close  to  the  orbit 
of  Jupiter,  and  are  now  recognized  and  spoken  of  as  Jupiter's 
"  family  of  comets  "  ;  eighteen  of  them  are  known  at  present. 
Similarly,  Saturn  is  credited  with  two  comets,  and  Uranus 
with  three,  one  of  them  being  Tempel's  comet,  which  is  closely 
connected  with  the  November  meteors,  and  is  due  on  its  next 
return  in  1900.  Finally,  Neptune  has  a  family  of  six,  among 
them  Halley's  comet,  and  two  others  which  have  returned  a 
second  time  to  perihelion  since  1880. 

298.  The  Capture  Theory.  —  The  generally  accepted  theory 
as  to  the  origin  of  these  "  comet-families  "  is  one  first  suggested 
by  Laplace  nearly  100  years  ago,  — that  the  comets  which  com- 
pose them  have  been  captured  by  the  planet  to  which  they 
stand  related.  A  comet  entering  the  system  in  a  parabolic 
orbit,  and  passing  near  a  planet,  will  be  disturbed,  —  either 
accelerated  or  retarded.  If  it  is  accelerated,  it  is  easy  to 
prove  that  the  original  parabolic  orbit  will  be  changed  to  an 
hyperbola,  and  the  comet  will  never  be  seen  again,  but  will 
pass  out  of  the  system  forever ;  but  if  it  is  retarded,  the  orbit 
becomes  elliptical)  and  the  comet  will  return  at  each  successive 
revolution  to  the  place  where  it  was  first  disturbed. 

But  this  is  not  the  end.  After  a  certain  number  of  revo- 
lutions, the  planet  and  the  comet  will  come  together  a  second 
time  at  or  near  the  place  where  they  met  before.  The  result 
may  then  be  an  acceleration,  which  will  send  the  comet  out 
of  the  system  finally ;  but  it  is  an  even  chance  at  least,  that 
it  may  be  a  second  retardation,  and  that  the  orbit  and  period 
may  thus  be  further  diminished  :  and  this  may  happen  over  and 
over  again,  until  the  comet's  orbit  falls  so  far  inside  that  of  the 


§  298]  THE   LEXELL-BROOKS   COMET.  215 

planet  that  there  is  no  further  disturbance  to  speak  of.  Given 
time  enough  and  comets  enough,  and  the  result  would  inevi- 
tably be  such  a  comet-family  as  really  exists.  We  may  add 
that  certain  researches  of  Professor  Newton  of  New  Haven 
and  others,  upon  the  position  and  distribution  of  cometary 
orbits,  decidedly  favor  the  idea  that  these  bodies  do  not 
originate  in  the  solar  system,  but  come  to  us  from  interstellar 
space. 

The  late  R.  A.  Proctor  declined  to  accept  this  capture  theory,  and 
maintained  with  much  vigor  and  ability  the  theory  that  comets  and 
meteor-swarms  have  been  ejected  from  the  great  planets  by  eruptions 
of  some  sort.  We  cannot  take  space  here  to  discuss  the  theory,  which 
is  really  not  quite  so  wild  as  at  first  it  seems ;  but  the  objections  to  it 
are  serious,  and  we  think  fatal. 

299.  The  Lexell-Brooks  Comet.  —  The  "  capture "  theory 
has  recently  received  a  remarkable  corroboration  in  the  case 
of  a  little  comet,  1889  V,  discovered  by  Mr.  Brooks  of  Geneva, 
N.Y.,  in  July,  1889.  It  was  soon  found  to  be  moving  with  a 
period  of  about  seven  years,  in  an  elliptical  orbit  which  passes 
very  near  to  that  of  Jupiter.  (We  remark  in  passing  that 
this  comet  in  August  divided  into  four  fragments ;  see  Art. 
314.)  On  investigating  the  orbit  more  carefully,  Mr.  S.  C. 
Chandler  of  Cambridge  (U.S.)  discovered  that,  in  1886,  the 
comet  and  the  planet  had  been  close  together  for  some  months, 
and  that  as  a  consequence  the  comet's  orbit  must  have  been 
completely  transformed,  the  previous  orbit  having  been  a  much 
larger  one  with  a  period  of  nearly  twenty-seven  years. 

Now,  in  1770,  a  famous  comet  appeared,  which  is  known  as 
LexelFs,  because  Lexell  computed  its  orbit.  It  was  bright, 
and  came  very  near  the  earth,  and,  according  to  Lexell' s  cal- 
culations, was  then  moving  in  an  orbit  with  a  period  of  only  five 
and  a  half  years,  —  the  first  instance  of  a  short-period  comet  on 
record ;  but  it  was  never  seen  again.  Its  failure  to  reappear, 
in  1776,  was  easily  accounted  for  by  the  fact  that  its  orbit  did 


216  PHYSICAL   CONSTITUTION   OF   COMETS.  [§  299 

not  then  bring  it  anywhere  near  the  earth.  But  it  should 
have  reappeared  in  1781,  and  for  a  long  time  its  disappear- 
ance was  very  mysterious,  until  Laplace,  some  years  later, 
showed  that,  in  1779,  the  comet  must  have  come  very  close 
to  Jupiter,  perhaps  as  near  as  some  of  its  satellites,  and  that 
in  consequence  the  attraction  of  that  planet  had  probably 
sent  it  into  a  new  orbit,  not  observable  from  the  earth. 

More  recent  investigations  by  Leverrier,  some  thirty  years 
ago,  show  that  while  the  data  are  insufficient  to  determine  the 
comet's  subsequent  orbit  with  certainty,  one  of  the  possible 
orbits  would  have  had  a  period  a  little  less  than  twenty-seven 
years.  This  would  bring  it  back,  in  1886,  after  four  revolu- 
tions, to  the  same  place  which  it  had  occupied  in  1779 ;  now 
nine  of  Jupiter's  periods  are  106|-  years,  so  that  he,  also,  would 
have  returned  to  the  same  place. 

To  make  a  long  story  short,  Mr.  Chandler  shows  that  it  is 
extremely  probable  that  Brooks's  comet,  1889  V,  is  identical 
with  Lexell's  comet  of  1770.  Jupiter  first  transformed  its 
orbit  from  a  parabola  to  an  ellipse,  with  a  period  of  five  and  a 
half  years ;  then  removed  it  from  our  sphere  of  observation ; 
and,  again,  after  a  century'  or  more,  has  brought  it  back. 
What  will  happen  at  the  next  encounter  of  the  comet  with  the 
planet  it  is  not  yet  possible  to  predict. 

PHYSICAL  CONSTITUTION  OF  COMETS. 

300.  Constituent  Parts  of  a  Comet.  —  (a)  The  essential  part 
of  a  comet,  that  which  is  always  present  and  gives  the  comet 
its  name,  is  the  coma,  or  nebulosity,  a  hazy  cloud  of  faintly 
luminous  transparent  matter. 

(b)  Next  we  have  the  nucleus,  which,  however,  is  wanting 
in  many  comets,  and  makes  its  appearance  only  as  the  comet 
comes  near  the  sun.  It  is  a  bright,  more  or  less  star-like 
point  near  the  centre  of  the  comet.  In  some  cases  it  is  double, 
or  even  multiple. 


§  300]  DIMENSIONS  OF  COMETS.  217 

(c)  The  tail  or  train  is  a  stream  of  light  which  commonly 
accompanies  a  bright  comet,  and  is  sometimes  present  even 
with  a  telescopic  one.     As  the  comet  approaches  the  sun,  the 
tail  follows  it ;  but  as  the  comet  moves  away  from  the  sun,  it 
precedes.     It  is  always,  speaking  broadly,  directed  away  from 
the  sun,  though  its  precise  form  and  position  are  determined 
partly  by  the  comet's  motion.     It  is  practically  certain  that 
it  consists  of  extremely  rarefied  matter  which  is  thrown  off  by 
the  comet  and  powerfully  repelled  by  the  sun. 

It  certainly  is  not  —  like  the  smoke  of  a  locomotive  or  train  of  a 
meteor  —  simply  left  behind  by  the  comet,  because  as  the  comet  is 
receding,  from  the  sun  the  tail  goes  before  it,  as  has  been  said. 

(d)  Jets   and  Envelopes.  —  The  head  of  a  comet   is   often 
veined  by  short  jets  of  light,  which  appear  to  be  spurted  out 
from  the  nucleus ;   and  sometimes  the  nucleus   throws  off  a 
series  of  concentric  envelopes,  like  hollow  shells,  one  within 
the  other.     These  phenomena,  however,  are  seldom  observed 
in  telescopic  comets. 

301.  Dimensions  of  Comets.  —  The  volume  or  bulk  of  a  comet 
is  often  enormous,  almost  inconceivably  so,  if  the  tail  is  in- 
cluded in  the  estimate.  The  head,  as  a  rule,  is  from  40,000  to 
50,000  miles  in  diameter  (comets  less  than  10,000  miles  in 
diameter  would  stand  little  chance  of  discovery).  Comets 
exceeding  150,000  miles  are  rather  rare,  though  there  are 
several  on  record. 

The  comet  of  1811  at  one  time  had  a  diameter  of  fully  1,200000 
miles,  40  per  cent  larger  than  that  of  the  sun.  The  head  of  the  comet 
of  1680  was  600,000  miles  in  diameter,  and  that  of  Donati's  comet,  of 
1858,  about  250,000. 

The  diameter  of  the  head  keeps  changing  all  the  time ;  and 
what  is  singular  is  that  while  the  comet  is  approaching  the 
sun  the  head  usually  contracts,  and  expands  again  as  it  recedes. 


218  MASS   OF   COMETS.  [§  3°1 

No  entirely  satisfactory  explanation  is  known  for  this  behavior,  but 
Sir  John  Herschel  has  suggested  that  the  change  is  merely  optical ; 
that  near  the  sun  a  part  of  the  nebulous  matter  is  evaporated  by  the 
solar  heat  and  so  becomes  invisible,  condensing  and  reappearing  again 
when  the  comet  gets  to  cooler  regions. 

The  nucleus  ordinarily  has  a  diameter  ranging  from  100  miles 
up  to  5000  or  6000,  or  even  more.  Like  the  comet's  head  it 
also  varies  greatly  in  diameter,  even  from  day  to  day,  so  that  it 
is  probably  not  a  solid  body.  Its  changes,  however,  do  not 
seem  to  depend  in  any  regular  'way  upon  the  comet's  distance 
from  the  sun,  but  rather  upon  its  activity  in  throwing  off  jets 
and  envelopes. 

The  tail  of  a  comet,  as  regards  simple  magnitude,  is  by 
far  the  most  imposing  feature.  Its  length  is  seldom  less 
than  from  5,000000  to  10,000000  miles.  It  frequently  attains 
50,000000,  and  there  are  several  cases  where  it  has  exceeded 
100,000000;  while  its  diameter  at  the  end  remote  from  the 
comet  varies  from  1,000000  to  15,000000. 

302.  Mass  of  Comets. — While  the  bulk  of  comets  is  thus 
enormous,  their  masses  are  apparently  insignificant,  in  no  case 
at  all  comparable  with  that  of  our  little  earth,  even.  The  evi- 
dence on  this  point,  however,  is  purely  negative ;  it  does  not 
enable  us  in  any  case  to  say  just  what  the  mass  really  is,  but 
only  to  say  how  great  it  is  not;  i.e.,  it  only  proves  that  a 
comet's  mass  is  less  than  1 0  ^  0  ^  of  the  earth's,1  —  how  much 
less  we  cannot  yet  find  out.  The  evidence  is  derived  from  the 
fact  that  no  sensible  perturbations  are  produced  in  the  motions 
of  a  planet  when  a  comet  comes  even  very  near  it,  although 
in  such  a  case  the  comet  itself  is  fairly  "sent  kiting,"  thus 
showing  that  gravitation  has  its  full  effect  between  the  two 
bodies. 

1  One  one-hundred-thousandth  of  the  earth's  mass  is  about  ten  times 
the  mass  of  the  earth's  whole  atmosphere,  and  is  equivalent  to  the  mass 
of  an  iron  ball  about  150  miles  in  diameter. 


§  302]  DENSITY   OF   COMETS.  219 

Lexell's  comet,  in  1770,  and  Biela's  comet  on  several  occasions, 
have  come  so  near  the  earth  that  the  length  of  the  comet's  period  was 
changed  by  several  weeks,  while  the  year  was  not  altered  by  so  much 
as  a  single  second.  It  would  have  been  changed  by  many  seconds  if 
the  comet's  mass  were  as  much  as  that  of  the  earth. 


303.  Density  of  Comets.  —  This  is,  of  course,  almost  incon- 
ceivably small,  the  mass  of  comets  being  so  minute  and  their 
volumes  so  enormous.  If  the  head  of  a  comet,  50,000  miles  in 
diameter,  has  a  mass  yrnnnnF  ^at  °^  the  eartn>  ^s  mean  density 
must  be  about  -g-^-tf  that  of  the  air  at  the  sea-level,  —  far  below 
that  of  the  best  air-pump  vacuum.  As  for  the  tail,  the  density 
must  be  almost  infinitely  lower  yet.  It  is  nearer  to  an  "  airy 
nothing  "  than  anything  else  we  know  of. 

The  extremely  low  density  of  comets  is  shown  also  by  their 
transparency.  Small  stars  can  be  seen  through  the  head  of  a 
comet  100,000  miles  in  diameter,  even  very  near  its  nucleus, 
and  with,  hardly  a  perceptible  diminution  of  their  lustre. 

We  must  bear  in  mind,  however,  that  the  low  mean  density  of  a 
comet  does  not  necessarily  imply  a  low  density  of  its  constituent  parti- 
cles. A  comet  may  be  to  a  considerable  extent  composed  of  small 
heavy  bodies,  and  still  have  a  low  mean  density,  provided  they  are  far 
enough  apart.  There  is  much  reason,  as  we  shall  see,  for  supposing 
that  such  is  really  the  case,  —  that  the  comet  is  largely  composed  of 
small  meteoric  stones,  carrying  with  them  a  certain  quantity  of  envel- 
oping gas. 

Another  point  should  be  referred  to.  Students  often  find  it 
impossible  to  conceive  how  such  impalpable  "dust  clouds" 
can  move  in  orbits  like  solid  masses,  and  with  such  enormous 
velocities.  They  forget  that  in  a  vacuum  a  feather  falls  as 
swiftly  as  a  stone.  Interplanetary  space  is  a  vacuum  far 
more  perfect  than  anything  we  can  produce  by  air-pumps,  and 
in  it  the  lightest  bodies  move  as  freely  and  swiftly  as  the 
densest,  since  there  is  nothing  to  resist  their  motion.  If  all 
the  earth  were  suddenly  annihilated  except  a  single  feather, 


220 


THE  LIGHT   OF   COMETS. 


[§303 


the  feather  would  keep  right  on  and  continue  the  same  orbit, 
with  unchanged  speed. 

304.  The  Light  of  Comets.  — To  some  extent  their  light 
may  be  mere  reflected  sunlight;  but  in  the  main  it  is  light 
emitted  by  the  comet  itself  under  the  stimulus  of  solar  action. 
That  the  light  depends  in  some  way  on  the  sun  is  shown  by 


FIG.  60.  — Comet  Spectra. 

(For  convenience  in  engraving,  the  dark  lines  of  the  solar  spectrum  in  the  lowest  strip 
of  the  figure  are  represented  as  bright.) 

the  fact  that  its  brightness  usually  varies  with  its  distance 
from  the  sun,  according  to  the  same  law  as  that  of  a  planet. 

But  the  brightness  frequently  varies  rapidly  and  capri- 
ciously without  any  apparent  reason ;  and  that  the  comet  is 
self-luminous  when  near  the  sun  is  proved  by  its  spectrum, 
which  is  not  at  all  like  the  spectrum  of  reflected  sunlight,  but 
is  a  spectrum  of  bright  bands,  three  of  which  are  usually  seen, 


304] 


DONATI  S   COMET. 


221 


and  have  been  identified  repeatedly  and  certainly  with  the 
spectrum  of  gaseous  hydrocarbons.  (All  the  different  hydro- 
carbon gases  give  the  same  spectrum  at  the  temperature  of  a 
Bunsen  burner.)  This  spectrum  is  absolutely  identical  with 
that  given  by  the  blue  base  of  a  candle  flame,  or,  better,  by 
a  Bunsen  burner  consuming  ordinary  coal  gas. 

Occasionally  a  fourth  band  is  seen  in  the  violet,  and  when  the 
comet  approaches  unusually  near  the  sun,  the  bright  lines  of  sodium, 
and  other  metals  (probably  iron),  sometimes  appear.  There  seem  to 
be  cases,  also,  when  different  bands  replace  the  ordinary  ones.  Fig.  60 
represents  the  ordinary  comet  spectrum,  compared  with  the  solar  spec- 


FIG.  61.  — Head  of  Donati's  Comet,  Oct.  5,  1858.     (Bond.) 

trum  and  with  that  of  a  candle  flame.  Two  anomalous  comet-spectra 
are  also  shown  in  the  figure.  The  spectrum  makes  it  almost  cer- 
tain that  hydrocarbon  gases  are  present  in  considerable  quantity, 


222 


FORMATION   OF   TAIL. 


[§304 


and  that  these  gases  are  somehow  rendered  luminous ;  not  probably 
by  any  general  heating,  however,  for  there  is  no  reason  to  think  that 
the  general  temperature  of  a  comet  is  very  high.  We  must  not  infer 
that  the  hydrocarbon  gas,  because  it  is  so  conspicuous  in  the  spec- 
trum, necessarily  constitutes  most  of  the  comet's  mass:  more  likely 
it  is  only  a  very  small  fraction  of  the  whole. 

305.  Phenomena  that  accompany  a  Comet's  Approach  to  the 
Sun.  —  When  the  comet  is  first  discovered,  it  is  usually  a  mere 
round,  hazy  cloud  of  faint  nebulosity,  a  little  brighter  near  the 
middle.  As  it  approaches  the  sun  it  brightens  rapidly,  and 
the  nucleus  appears.  Then  on  the  sunward  side  the  nucleus 
begins  to  emit  luminous  jets,  or  else  to  throw  off  more  or  less 
symmetrical  envelopes,  which  follow  each  other  at  intervals  of 
some  hours,  expanding  or  growing  fainter,  until  they  are  lost 
in  the  nebulosity  of  the  head. 

Fig.  61  shows  the  envelopes  as  they  appeared  in  the  head  of 
Donati's  comet  of  1858.  At  one  time  seven  of  them  were  vis- 
ible together  :  very  few  com- 
ets, however,  exhibit  this  phe- 
nomenon with  such  symmetry. 
More  frequently  the  emissions 
from  the  nucleus  take  the  form 
of  jets  and  streamers. 


To  Sun 


306.   Formation  of  Tail. — 

The  tail  appears  to  be  formed 
of  material  which  is  first  pro- 
jected from  the  nucleus  of  the 
comet  towards  the  sun,  and 
then  afterwards  repelled  by 
the  sun,  as  illustrated  by  Fig. 
62.  At  least  this  theory  has 
the  great  advantage  over  all  others  which  have  been  proposed 
that  it  not  only  accounts  for  the  phenomenon  in  a  general  way, 
but  admits  of  being  worked  out  in  detail  and  verified  mathe- 


FIG.  62.  —  Formation  of  a  Comet's  Tail  by 
Matter  expelled  from  the  Head. 


§  306]  TYPES   OF   COMETS'   TAILS.  223 

matically,  by  comparing  the  actual  size  and  form  of  the  planet's 
tail,  at  different  points  in  the  orbit,  with  that  indicated  by  the 
theory  j  and  the  accordance  is  generally  very  satisfactory. 

The  tail  is  curved  because  the  repelled  particles,  after  leav- 
ing the  comet's  head,  retain  their  original  motion,  so  that  they 
are  arranged  not  along  a  straight  line  drawn  from  the  sun  to 


FIG.  63.  —  A  Comet's  Tail  at  Different  Points  in  its  Orbit  near  Perihelion. 

the  comet,  but  on  a  curve  convex  to  the  comet's  motion,  as 
shown  in  Fig.  63 ;  but  the  stronger  the  repulsion  the  less  the 
curvature,  and  the  straighter  the  tail.  The  nature  of  the  force 
which  repels  the  particles  of  a  comet  is,  of  course,  only  a 
matter  of  speculation ;  but  the  idea  that  it  is  electrical  gener- 
ally prevails,  though  the  detailed  explanation  is  not  easy. 
There  is  no  reason  to  suppose  that  the  matter  driven  off  to 
form  the  tail  is  ever  recovered  by  the  comet. 

307.  Types  of  Comets'  Tails. — Bredichin,  of  Moscow,  has 
found  that  the  trains  of  comets  may  be  classified  under  three 
different  types,  as  indicated  by  Fig.  64. 

First,  the  long,  straight  rays,  composed  of  matter  upon  which  the 
solar  repulsion  is  from  ten  to  fifteen  times  as  great  as  the  attraction 


224 


TYPES  OF  COMETS'  TAILS. 


[§307 


enormous. 


of  gravity,  so  that  the  particles  leave  the  comet  with  a  velocity  of  four 
or  five  miles  a  second,  which  is  afterwards  increased  until  it  becomes 
The  nearly  straight  rays,  shown  in  Fig.  58,  belong  to 

this  type.  For  plausible 
reasons,  which,  however, 
we  cannot  stop  to  explain, 
Bredichin  supposes  these 
straight  rays  to  be  com- 
posed of  hydrogen. 

The  second  type  is  the 
ordinary,  curved,  plume- 
like  train,  like  the  principal 
tail  of  Donati's  comet.  In 
trains  of  this  type,  sup- 
posed to  be  due  to  hydro- 
carbon vapors,  the  repulsive 
force  varies  from  2.2  times 
the  attraction  of  gravity  for 
particles  on  the  convex  edge 
of  the  train,  to  half  that 
amount  for  those  on  the 
inner  edge.  The  spectrum 
is  the  same  as  that  of  the 
comet's  head. 

Third,  a  few  comets  show 
tails  of  still  a  third  type,  — 
short,  stubby  brushes,  vio- 
lently curved,  and  due  to 
matter  on  which  the  repul- 
sive force  is  feeble  as  com- 
pared with  gravity.  These 
are  assigned  by  Bredichin 
to  metallic  vapors  of  con- 
siderable density,  with  an 
FIG.  64.  ,  .  ,  .  •;. 

admixture  of  sodium,  etc. 

Bredichin's  Three  Types  of  Cometary  Tails. 


308.  Unexplained  and  Anomalous  Phenomena.  —  A  curious 
phenomenon,  not  yet  explained,  is  the  dark  stripe  which,  in  a 


§308]  THE  NATURE  OF  COMETS.  225 

large  comet  approaching  the  sun,  runs  down  the  centre  of  the 
tail,  looking  very  much  as  if  it  were  a  shadow  of  the  comet's 
head.  It  is  certainly  not  a  shadow,  however,  because  it  usually 
makes  more  or  less  of  an  angle 
with  the  sun's  direction.  It  is 
well  shown  in  Fig.  61.  When  the 
comet  is  at  a  greater  distance  from 
the  sun,  this  central  stripe  is  usu- 
ally bright,  as  in  Fig.  65. 

Not    unfrequently,    moreover,  FIG.  65. 

COmetS  pOSSeSS  anomalous  tails, —  Bright-centred  Tail  of  Coggia's  Comet, 
,  .,  ,.  .j  .  ,  ,  June,  1874. 

tails  directed  sometimes  straight 

towards  the  sun,  and  sometimes  at  right  angles  to  that  direc- 
tion. Then  sometimes  there  are  luminous  sheaths,  which  seem 
to  envelop  the  head  of  the  comet  and  project  towards  the  sun 
(Fig.  66),  or  little  clouds  of  cometary  matter  which  leave  the 
main  comet  like  puffs  of  smoke  from  a  bursting  bomb,  and 
travel  off  at  an  angle  until  they  fade  away  (see  Fig.  66). 
None  of  these  appearances  are  contradictory  to  the  theory 
above  stated,  though  they  are  not  yet  clearly  included 
in  it. 

309.  The  Nature  of  Comets.  —  All  things  considered,  the 
most  probable  hypothesis  as  to  the  constitution  of  a  comet,  so 
far  as  we  can  judge  at  present,  is  that  its  head  is  a  swarm  of 
small  meteoric  particles,  widely  separated  (say  pin-heads,  many 
yards  apart),  each  carrying  with  it  an  envelope  of  rarefied  gas 
and  vapor,  in  which  light  is  produced  either  by  electric  dis- 
charges between  the  solid  particles,  or  by  some  action  due  to 
the  rays  of  the  sun.  As  to  the  size  of  the  constituent  par- 
ticles, opinions  differ  widely.  Some  maintain  that  they  are 
large  rocks :  Professor  Newton  calls  a  comet  a  "  gravel  bank  " : 
others  say  that  it  is  a  mere  "dust-cloud."  The  unquestion- 
able close  connection  between  meteors  and  comets  (Art.  327) 
almost  compels  some  "  meteoric  hypothesis." 


226  DANGER   FROM  COMETS.  [§  310 

310.  Danger  from  Comets.  —  In  all  probability  there   is   none. 
It  has  been  supposed  that  comets  might  do  us  harm  in  two  ways, — 
either  by  actually  striking  the  earth,  or  by  falling  into  the  sun  and 
thus  producing  such  an  increase  of  solar  heat  as  to  burn  us  up. 

As  regards  the  possibility  of  a  collision  between  a  comet  and  the 
earth,  the  event  is  certainly  possible.  In  fact,  if  the  earth  lasts  long 
enough,  it  is  practically  sure  to  happen,  for  there  are  several  comet's 
orbits  which  pass  nearer  to  the  earth's  orbit  than  the  semi-diameter 
of  the  comet's  head.  As  to  the  consequence  of  such  a  collision,  it  is 
impossible  to  speak  with  absolute  confidence  for  want  of  certain  knowl- 
edge as  to  the  constitution  of  a  comet.  If  the  theory  presented  in  the 
preceding  article  is  true,  everything  depends  on  the  size  of  the  separate 
solid  particles  which  form  the  main  portion  of  the  comet.  If  they 
weigh  tons,  the  bombardment  experienced  by  the  earth  when  struck 
by  the  comet  would  be  a  very  serious  matter.  If  they  are  most  of 
them  not  larger  than  pin-heads,  the  result  would  be  only  a  meteoric 
shower. 

The  encounters,  however,  will  be  very  rare.  If  we  accept  the  esti- 
mate of  Babinet,  they  will  occur  on  the  average  once  in  about 
15,000000  years. 

If  a  comet  actually  strikes  the  sun,  which  would  necessarily  be  a 
very  rare  phenomenon,  it  is  not  likely  that  the  least  harm  will  be 
done.  The  collision  might  generate  about  as  much  heat  as  the  sun 
radiates  in  eight  or  nine  hours;  but  the  cometary  particles  would 
pierce  the  photosphere,  and  their  heat  would  be  liberated  mostly  below 
the  solar  surface,  simply  expanding  by  some  slight  amount  the  diam- 
eter of  the  sun,  but  making  no  particular  difference  in  the  amount  of 
its  radiation  for  the  time  being.  There  might  be,  and  very  likely 
would  be,  a  flash  of  some  kind  at  the  solar  surface  when  the  shower 
of  meteors  struck  it ;  but  probably  nothing  that  the  astronomer  would 
not  take  delight  in  observing. 

311.  Remarkable  Comets.  —  Our  space  does  not  permit  us 
to  give  full  accounts  of  any  considerable  number.     We  limit 
ourselves   to   two,  which  for  various   reasons  are  of  special 
interest. 

Biela's  comet  is,  or  rather  was,  a  small  comet  some  40,000 
miles  in  diameter,  at  times  barely  visible  to  the  naked  eye, 


§  311]  BIELA'S  COMET.  227 

and  sometimes  showing  a  short  tail.  It  had  a  period  of  6.6 
years,  and  was  the  second  comet  of  short  period  known,  hav- 
ing been  discovered  by  Biela,  an  Austrian  officer,  in  1826 
(the  periodicity  of  Encke's  comet  had  been  discovered  seven 
years  earlier).  Its  orbit  comes  within  a  few  thousand  miles 
of  the  earth's  orbit,  the  distance  varying  somewhat,  of  course, 
on  account  of  perturbations ;  but  the  approach  is  sometimes 
so  close  that,  if  the  comet  and  the  earth  should  happen  to 
arrive  at  the  same  time,  there  would  be  a  collision.  At  its 
return,  in  1846,  it  split  into  two.  When  first  seen  on  Nov.  28th, 
it  was  one  and  single.  On  Dec.  19th  it  was  distinctly  pear- 
shaped,  and  ten  days  later  it  was  divided. 

The  twin  comets  travelled  along  for  four  months,  at  an  almost 
unchanging  distance  of  about  165,000  miles,  without  any  apparent 
effect  upon  each  other's  motions,  but  both  very  active  from  the  physical 
point  of  view,  showing  remarkable  variations  and  alterations  of  bright- 
ness entirely  unexplained.  In  August,  1852,  the  twins  were  again 
observed,  then  separated  by  a  distance  of  about  1,500000  miles;  but 
it  was  impossible  to  tell  which  was  which.  Neither  of  them  has  ever 
been  seen  again,  though  they  must  have  returned  many  times,  and 
more  than  once  in  a  very  favorable  position. 

312.  There  remains,  however,  another  remarkable  chapter 
in  the  story  of  this  comet.  In  1872,  on  Nov.  27th,  just  as  the 
earth  was  crossing  the  track  of  the  lost  comet,  but  some  mil- 
lions of  miles  behind  where  the  comet  ought  to  be,  she  en- 
countered a  wonderful  meteoric  shower.  As  Miss  Clerke 
expresses  it,  perhaps  a  little  too  positively,  "  it  became  evident 
that  Biela's  comet  was  shedding  over  us  the  pulverized  prod- 
ucts of  its  disintegration."  A  similar  meteoric  shower  oc- 
curred again  in  1885,  when  the  earth  once  more  crossed  the 
track  of  the  comet. 

It  is  not  certain  whether  the  meteor  swarms  thus  encountered  were 
the  remains  of  the  comet  itself,  or  whether  they  were  other  small  bodies 
merely  following  in  its  path.  The  comet  must  have  been  several  mil- 


228  THE   GREAT   COMET   OF  1882.  [§  312 

lions  of  miles  ahead  of  the  place  where  these  meteor  swarms  were 
met,  unless  it  has  been  set  back  in  its  orbit  since  1852  by  some  unex- 
plained and  improbable  perturbations.  But  the  comet  cannot  be 
found,  and  if  it  still  exists  and  occupies  the  place  it  ought  to,  it  must 
have  somehow  lost  the  power  of  shining. 

313.  The  Great  Comet  of  1882.  — This  is  the  most  recent 
of  the  brilliant  comets  that  have  been  observed,  and  will  long 
be  remembered  not  only  for  its  magnificent  beauty,  but  for  the 
great  number  of  unusual  phenomena  which  it  presented.     It 
was  first  seen  in  the  southern  hemisphere  about  Sept.  3d,  but 
not  in  the  northern  until  the  17th,  the  day  on  which  it  arrived 
at  perihelion.     On  that  day  it  was  independently  discovered 
within  2°  or  3°  of  the  sun,  near  noon,  by  several  observers,  who 
had  not  before  heard  of  its  existence.     It  was  visible  to  the 
naked  eye  in  full  sunshine  for  more  than  a  week  after  its  peri- 
helion passage.     It  then  became  a  splendid  object  in  the  morn- 
ing sky,  and  continued  to  be  observed  for  six  months. 

That  portion  of  the  orbit  visible  from  the  earth  coincides 
almost  exactly  with  the  orbits  of  four  other  comets,  —  those 
of  1668,  1843,  1880,  and  1887,  with  which  it  forms  a  "  comet 
group,"  as  already  mentioned  (Art.  294).  The  perihelion  dis- 
tances of  the  comets  of  this  group  are'  all  less  than  750,000 
miles,  so  that  they  pass  within  300,000  miles  of  the  sun's 
surface ;  i.e.,  right  through  the  corona,  and  with  a  velocity 
exceeding  300  miles  a  second ;  and  yet  this  passage  through 
the  corona  does  not  disturb  their  motion  perceptibly. 

The  orbit  of  the  comet  of  1882  turns  out  to  be  a  very  elon- 
gated ellipse  with  a  period  of  about  800  years.  The  period  of 
the  comet  of  1880  appears  to  be  only  seventeen  years,  while 
the  orbits  of  the  other  three  are  sensibly  parabolic. 

314.  Early  in  October  the  comet  presented  the   ordinary 
features.     The  nucleus  was  round,  a  number  of  well-marked 
envelopes  were  visible  in  the  head^  and  the  dark  stripe  down 


§  314] 


THE   "SHEATH. 


the  centre  of  the  tail  was  sharply  defined.  Two  weeks  later 
the  nucleus  had  been  broken  up  and  transformed  into  a 
crooked  stream,  some  50,000  miles  in  length,  of  five  or  six 
bright  points  :  the  envelopes  had  vanished  from  the  head,  and 
the  dark  stripe  was  replaced  by  a  bright  central  spine. 

At  the  time  of  perihelion  the  comet's  spectrum  was  filled 
with  countless  bright  lines.  Those  of  sodium  were  easily 
recognizable,  and  continued  visible  for  weeks ;  the  other  lines 


Fio.  66.  — The  "  Sheath,"  and  the  Attendants  of  the  Comet  of  1882. 

continued  only  a  few  days  and  were  not  certainly  identified, 
although  the  general  aspect  of  the  spectrum  indicated  that 
iron,  manganese,  and  calcium  were  probably  present.  By  the 
middle  of  October  it  had  become  simply  the  normal  comet 
spectrum,  with  the  ordinary  hydrocarbon  bands. 


230  METEORS   AND   SHOOTING-STARS.  [§  3*4 

The  comet  was  so  situated  that  the  tail  was  directed  nearly 
away  from  the  earth,  and  so  was  not  seen  to  good  advantage, 
never  having  an  apparent  length  exceeding  35°.  The  actual 
length,  however,  at  one  time  was  more  than  100,000000  miles. 

A  unique,  and  so  far  unexplained,  phenomenon  was  a  faint, 
straight-edged  "sheath"  of  light,  which  enveloped  the  por- 
tions of  the  comet  near  the  head,  and  projected  3°  or  4°  in 
front  of  it,  as  shown  in  Fig.  66.  Moreover,  there  were  certain 
shreds  of  cometary  matter  accompanying  the  comet,  at  a  dis- 
tance of  3°  or  4°  when  first  seen,  but  gradually  receding  and 
growing  fainter.  This  also  was  something  new  in  cometary 
history,  though  the  Lexell-Brooks  comet,  1889  V,  has  since 
done  the  same  thing. 


METEORS  AND   SHOOTING-STARS. 


315.  Meteorites.  —  Occasionally  bodies  fall  upon  the 
out  of  the  sky.  Such  a  body  during  its  flight  through  the  air 
is  called  a  "  Meteorite  "  or  "  Bolide,"  and  the  pieces  which  fall 
to  the  earth  are  called  "Meteorites,"  "Aerolites/'  "Urano- 
liths,"  or  simply  "meteoric  stones." 

If  the  fall  occurs  at  night,  a  ball  of  fire  is  seen,  which  moves 
with  an  apparent  velocity  depending  upon  the  distance  of  the 
meteor  and  the  direction  of  its  motion.  The  fire-ball  is  gener- 
ally followed  by  a  luminous  train,  which  sometimes  remains 
visible  for  many  minutes  after  the  meteor  itself  has  disap- 
peared. The  motion  is  usually  somewhat  irregular,  and  here 
and  there  along  its  path  the  meteor  throws  off  sparks  and  frag- 
ments, and  changes  its  course  more  or  less  abruptly.  Some- 
times it  vanishes  by  simply  fading  out  in  the  air,  sometimes 
by  bursting  like  a  rocket.  If  the  observer  is  near  enough,  the 
flight  is  accompanied  by  a  heavy,  continuous  roar,  emphasized 
now  and  then  by  violent  detonations. 

The  observer  must  not  expect  to  hear  the  explosion  at  the  moment 
when  he  sees  it,  since  sound  travels  only  about  twelve  miles  a  minute. 


315] 


THE  AEROLITES   THEMSELVES. 


231 


If  the  fall  occurs  by  day,  the  luminous  appearances  are 
mainly  wanting,  though  sometimes  a  white  cloud  is  seen,  and 
the  train  may  be  visible.  In  a  few  cases  aerolites  have  fallen 
almost  silently,  and  without  warning. 

316.  The  Aerolites  themselves.  —  The  mass  that  falls  is 
sometimes  a  single  piece,  but  more  usually  there  are  many 
fragments,  sometimes  numbering  thousands ;  so  that,  as  the 
old  writers  say,  "  it  rains  stones."  The  pieces  weigh  from  500 
pounds  to  a  few  grains, 
the  aggregate  mass 
sometimes  amounting 
to  a  number  of  tons. 
By  far  the  greater  num- 
ber of  aerolites  are 
stones,  but  a  few,  per- 
haps three  or  four  per 
cent  of  the  whole  num- 
ber, are  masses  of  near- 
ly pure  iron  more  or 
less  alloyed  with  nickel 

The  total  number  of 
meteorites  which  have 
fallen  and  been  gathered 
into  cabinets  since  1800 
is  about  250,  —  only  10 
of  which  are  iron  masses. 
Nearly  all,  however,  con- 
tain a  large  percentage  of 
iron,  either  in  the  metal- 
lic form  or  as  sulphide. 
Between  25  and  30  of  the 
250  fell  within  the  United  States,  the  most  remarkable  being  those 
of  Weston,  Conn.,  in  1807;  New  Concord,  Ohio,  1860;  Amana,  Iowa, 
1875 ;  Emmett  County,  Iowa,  1879  (mainly  iron)  ;  and  Johnson 
County,  Ark.,  1886  (iron). 


FIG.  67. 
Fragment  of  one  of  the  Amana  Meteoric  Stones. 


232  PATH  AND   MOTION.  [§  316 

Twenty-four  of  the  chemical  elements  have  been  found  in 
these  bodies,  but  not  one  new  element,  though  a  large  number 
of  new  minerals  appear  in  them,  and  seem  to  be  characteristic 
of  aerolites. 

The  most  distinctive  external  feature  of  a  meteorite  is  the 
thin,  black,  varnish-like  crust  that  covers  it.  It  is  formed  by 
the  melting  of  the  surface  during  the  meteor's  swift  flight 
through  the  air,  and  in  some  cases  penetrates  the  mass  in 
cracks  and  veins.  The  surface  is  generally  somewhat  uneven, 
having  "thumb-marks"  upon  it,  —  hollows,  probably  formed 
by  the  fusion  of  some  of  the  softer  minerals.  Fig.  67  is  from 
a  photograph  given  in  Langley's  "New  Astronomy,"  where 
the  body  is  designated,  perhaps  a  little  too  positively,  as  "  part 
of  a  comet." 

317.  Path  and  Motion.  — When  a  meteor  has  been  observed 
from  a  number  of  different  stations,  its  path  can  be  computed. 
It  usually  is  first  seen  at  an  altitude  of  between  80  and  100 
miles,  and  disappears  at  an  altitude  of  between  5  and  10. 
The  length  of  the  path  may  be  anywhere  from  50  to  500  miles. 
In  the  earlier  part  of  its  course,  the  velocity  ranges  from  10 
to  40  miles  a  second,  but  this  is  greatly  reduced  before  the 
meteor  disappears. 

In  observing  these  bodies,  the  object  should  be  to  obtain  as  accurate 
an  estimate  as  possible  of  the  altitude  and  azimuth  of  the  meteor,  at 
moments  which  can  be  identified,  and  also  of  the  time  occupied  in 
traversing  definite  portions  of  the  path.  The  altitude  and  azimuth 
will  enable  us  to  determine  the  height  and  position  of  the  meteor, 
while  the  observations  of  the  time  are  necessary  in  computing  its 
velocity.  By  night  the  stars  furnish  the  best  reference  points  from 
which  to  determine  its  position.  By  day,  one  must  take  advantage  of 
natural  objects  or  buildings  to  define  the  meteor's  place,  the  observer 
marking  the  precise  spot  where  he  stood.  By  taking  the  proper 
instrument  to  the  place  afterwards,  it  is  then  easy  to  ascertain  the 
bearings  and  altitude.  As  to  the  time  of  flight,  it  is  usual  for  the 
observer  to  begin  to  repeat  rapidly  some  familiar  verse  of  doggerel 


§  317]  LIGHT   AND   HEAT   OF  METEORS.  233 

when  the  meteor  is  first  seen,  reiterating  it  until  the  meteor  disap- 
pears. Then  by  rehearsing  the  same  before  a  clock,  the  number  of 
seconds  can  be  pretty  accurately  determined. 

318.  The   Light   and   Heat   of    Meteors.  —  These  are  due 
simply  to  the  destruction  of  the  meteor's  velocity  by  the  fric- 
tion and  resistance  of  the  air.     When  a  body  moving  with  a 
high  velocity  is  stopped  by  the  resistance  of  the  air,  by  far  the 
greater  part  of  its  energy  is  transformed  into  heat.     Sir  Wil- 
liam Thomson  has  shown  that  the  heating  effect  in  the  case  of 
a  body  moving  through  the  air  with  a  velocity  exceeding  ten 
miles  a  second,  is  the  same  as  if  it  were  "  immersed  in  a  flame 
having  a  temperature  at  least  as  high  as  the  oxyhydrogen 
blow-pipe " ;  and,  moreover,  this  temperature  is  independent 
of  the  density  of  the  air,  —  depending  only  on  the  velocity  of 
the  meteor.      Where  the  air  is  dense,  the  total  quantity  of 
heat  (i.e.,  the  number  of  calories  developed  in  a  given  time)  is 
of  course  greater  than  where  the  air  is  rarified ;  but  the  virtual 
temperature  of  the  air  itself  where  it  rubs  against  the  surface 
is  the  same  in  either  case.     During  the  meteor's  flight,  its  sur- 
face, therefore,  is  raised  to  a  white  heat  and  melted,  and  the 
liquefied  portions  are  swept  off  by  the  rush  of  air,  condensing 
as  they  cool  to  form  the  train.     In   some   cases   this  train 
remains   visible   for  many  minutes,  —  a  fact  not   easily  ex- 
plained.    It  seems  probable  that  the  material  must  be  phos- 
phorescent. 

319.  Origin  of  Meteors.  —  They  cannot  be,  as   some  have 
maintained,  the  immediate   product  of   eruptions  from  volca- 
noes, either  terrestrial  or  lunar,  since  they  reach  our  atmo- 
sphere with  a  velocity  which  makes  it  certain  that  they  come 
to  us  from  the  depths  of  space.     There  is  no  proof  that  they 
have  originated  in  any  way  different  from  the  larger  heavenly 
bodies.     At  the  same  time  many  of  them  resemble  each  other 
so  closely  as  almost  to  compel  the  surmise  that  these,  at  least, 


234  SHOOTING-STARS.  [§  319 

had  a  common  source.  It  is  not  perhaps  impossible  that  such 
may  be  fragments  which  long  ago  were  shot  out  from  now 
extinct  lunar  volcanoes,  with  a  velocity  which  made  planets 
of  them  for  the  time  being.  If  so,  they  have  since  been  trav- 
elling in  independent  orbits  until  they  encountered  the  earth 
at  the  point  where  her  orbit  crosses  theirs.  Nor  is  it  impos- 
sible that  some  of  them  were  thrown  out  by  terrestrial  erup- 
tions when  the  earth  was  young;  or  that  they  have  been 
ejected  from  the  planets,  or  even  from  the  stars.  It  is  only 
certain  that  during  the  period  immediately  preceding  their 
arrival  upon  the  earth,  they  have  been  travelling  in  long 
ellipses,  or  parabolas,  around  the  sun. 


SHOOTING-STARS. 

320.  Their  Nature  and  Appearance.  —  These  are  the  evanes- 
cent, swiftly  moving,  star-like  points  of  light  which  may  be 
seen  every  few  minutes  on  any  clear  moonless  night.     They 
make  no  sound,  nor  has  anything  been  known  to  reach  the 
earth's  surface  from  them. 

For  this  reason  it  is  probably  best  to  retain,  provisionally,  at  least, 
the  old  distinction  between  them  and  the  great  meteors  from  which 
aerolites  fall.  It  is  quite  possible  that  the  distinction  has  no  real 
ground,  —  that  shooting-stars,  as  is  maintained  by  many,  are  just  like 
other  meteors,  except  that  being  so  small  they  are  entirely  consumed 
in  the  air ;  but  then,  on  the  other  hand,  there  are  some  things  which 
rather  favor  the  idea  that  the  two  classes  differ  in  about  the  same  way 
as  asteroids  do  from  comets.  We  know  that  an  aerolitic  meteor  is  a 
compact  mass  of  rock.  It  is  possible,  or  even  likely,  that  a  shooting- 
star,  on  the  contrary,  is  a  little  dust-cloud,  —  like  a  puff  of  smoke. 

321.  Number    of    Shooting-stars.  —  Their  number  is   enor- 
mous.    A  single  observer  averages  from  four  to  eight  an  hour ; 
but  if  the  observers  are  sufficiently  numerous,  and  so  placed 
as  to  be  sure  of  noting  all  that  are  visible  from  a  given  station. 


§321]  ELEVATION",   PATH,   AND   VELOCITY.  235 

about  eight  times  as  many  are  counted.  From  this  it  has 
been  estimated  that  the  total  number  which  enter  our  atmo- 
sphere daily  must  be  between  10,000000  and  20,000000,  the 
average  distance  between  them  being  some  200  miles. 

Besides  those  which  are  visible  to  the  naked  eye,  there  is  a  still 
larger  number  of  meteors  which  are  so  small  as  to  be  observable  only 
with  the  telescope. 

The  average  hourly  number  about  6  o'clock  in  the  morning 
is  double  the  hourly  number  in  the  evening ;  the  reason  being 
that  in  the  morning  we  are  in  front  of  the  earth,  as  regards  its 
orbital  motion,  while  in  the  evening  we  are  in  the  rear.  In 
the  evening  we  see  only  such  as  overtake  us ;  in  the  morning 
we  see  all  that  we  either  meet  or  overtake. 

322.  Elevation,  Path,  and  Velocity.  —  By  observations  made 
at  stations  30  or  40  miles  apart,  it  is  easy  to  determine  these 
data  with  some  accuracy.     It  is  found  that  on  the  average  the 
shooting-stars  appear  at  a  height  of  about  74  miles,  and  dis- 
appear at  an  elevation  of  about  50  miles,  after  traversing  a 
course  40  or  50  miles  long,  with  a  velocity  from  10  to  50  miles 
a  second,  —  about  25  on  the  average.     They  do  not  begin  to 
be  visible  at  so  great  a  height  as  the  aerolitic  meteors ;  and 
they  are  more  quickly  consumed,  and  therefore  do  not  pene- 
trate the  atmosphere  so  deeply. 

323.  Brightness,   Material,   and  Mass.  —  Now  and  then  a 
shooting-star  rivals  Jupiter,  or  even  Venus,  in  brightness.     A 
considerable  number  are  like  first-magnitude  stars ;   but  the 
great   majority  are  faint.     The   bright   ones    generally  leave 
trains.     Occasionally  it  has   been   possible  to   get   a   "snap 
shot,"  so  to  speak,  at  the  spectrum  of  a  meteor,  and  in  it  the 
bright  lines  of  sodium  and  magnesium  (probably)  are  fairly 
conspicuous  among  many  others  which  cannot  be  identified  by 
such  a  hasty  glance. 


236          MATERIAL  AND   MASS   OF   SHOOTING-STARS.       [§  323 

Since  these  bodies  are  consumed  in  the  air,  all  that  we  can 
hope  to  get  of  their  material  is  their  "  ashes.'7 

In  most  places  its  collection  and  identification  is,  of  course,  hope- 
less ;  but  the  Swedish  naturalist  Nordenskiold  thought  that  it  might 
be  found  in  the  polar  snows.  In  Spitzbergen  he  therefore  melted 
several  tons  of  snow,  and  on  filtering  the  water  he  actually  detected 
in  it  a  sediment  containing  minute  globules  of  oxide  and  sulphide  of 
iron.  Similar  globules  have  also  been  found  in  the  products  of  deep- 
sea  dredging.  They  may  be  meteoric,  but  what  we  now  know  of  the 
distance  to  which  smoke  and  fine  volcanic  dust  is  carried  by  the  wind 
make  it  not  improbable  that  they  may  be  of  purely  terrestrial  origin. 

We  have  no  way  of  determining  the  exact  mass  of  a  shoot- 
ing-star, but  from  the  light  it  emits  as  seen  from  a  known  dis- 
tance, an  approximate  estimate  can  be  formed,  since  we  know 
roughly  how  much  energy  corresponds  to  the  production  of 
a  given  amount  of  light.  It  is  likely,  on  the  whole,  that  an 
ordinary  meteor  and  a  good  electric  incandescent  lamp  do  not 
differ  widely  in  what  is  called  their  'luminous  efficiency7;  i.e., 
the  percentage  of  their  total  energy  which  is  converted  into 
visible  light.  Calculations  on  this  basis  indicate  that  ordinary 
shooting-stars  are  very  minute,  weighing  only  a  small  fraction 
of  an  ounce,  —  from  less  than  a  grain  up  to  50  or  100  grains 
for  a  very  large  one. 

324.  Meteoric  Showers.  —  There  are  occasions  when  these 
bodies,  instead  of  showing  themselves  here  and  there  in  the 
sky  at  intervals  of  several  minutes,  appear  in  showers  of  thou- 
sands ;  and  at  such  times  they  do  not  move  at  random,  but  all 
their  paths  diverge  or  radiate  from  a  single  point  in  the  sky 
known  as  the  radiant;  i.e.,  their  paths  produced  backward  all 
pass  through  this  point,  though  they  do  not  usually  start 
there.  Meteors  which  appear  near  the  radiant  are  apparently 
stationary,  or  describe  paths  which  are  very  short,  while  those 
in  the  more  distant  regions  of  the  sky  pursue  long  courses. 
The  radiant  keeps  its  place  among  the  stars  sensibly  un- 


324] 


METEORIC   SHOWEBS. 


237 


changed  during  the  whole  continuance  of  the  shower ;  it  may 
be  for  hours  and  even  days,  and  the  shower  is  named  accord- 
ingly from  the  place  of  the  radiant.  Thus  we  have  the 


FIG.  68.  —  The  Meteoric  Radiant  in  Leo,  Nov.  13, 1866. 

"Leonids,"  or  meteors  whose  radiant  is  the  constellation  of 
Leo ;  the  "  Andromedes  "  (or  Bielids)  ;  the  "  Perseids  "  ;  the 
"Lyrids,"  etc. 

Fig.  68  represents  the  tracks  of  a  large  number  of  the  Leonids  of 
1866,  showing  the  positions  of  the  radiant  near  Zeta  Leonis. 

The  radiant  is  explained  as  a  mere  effect  of  perspective. 
The  meteors  are  all  moving  in  lines  nearly  parallel  with  each 
other  when  encountered  by  the  earth,  and  the  radiant  is 
simply  the  perspective  "  vanishing-point "  of  this  system  of 
parallels.  Its  position  depends  entirely  on  the  direction  of 
the  motion  of  the  meteors  with  respect  to  the  earth.  For 
various  reasons,  however,  the  paths  of  the  meteors,  after  they 


238  DATES   OF   METEORIC   SHOWERS.  [§  324 

enter  the  air,  are  not  exactly  parallel,  and  in  consequence  the 
radiant  is  not  a  mathematical  point,  but  a  "  spot "  in  the  sky, 
often  covering  an  area  of  3°  or  4°  square. 

Probably  the  most  remarkable  of  all  the  meteoric  showers 
that  ever  occurred  was  that  of  the  Leonids  on  Nov.  12th, 
1833.  The  number  of  meteors  at  some  stations  was  estimated 
as  high  as  100,000  an  hour,  for  five  or  six  hours.  "  The  sky 
was  as  full  of  them  as  it  ever  is  of  snow-flakes  in  a  storm." 

325.  Dates  of  Meteoric  Showers.  —  Such  meteoric  showers 
are  caused  by  the  earth's   encounter  with  a  swarm  of  little 
meteors ;  and  since  this  swarm  pursues  a  regular  orbit  around 
the  sun,  the  earth  can  meet  it  only  when  she  is  at  the  point 
where  her  orbit  cuts  this  path.      The   encounter,    therefore, 
must  always  happen  on  or  near  the  same  day  of  the  year, 
except  as  in  time  the  meteoric  orbits  shift  their  positions  on 
account  of  perturbations.      The   Leonid   showers,    therefore, 
always  appear  on  the  13th  of  November,  within  a  day  or  two ; 
and  the  Andromedes  on  the  27th  or  28th  of  the  same  month. 

In  some  cases  the  meteors  are  distributed  along  their  whole 
orbit,  forming  a  sort  of  elliptical  ring,  and  are  rather  widely 
scattered.  In  that  case  the  shower  recurs  every  year,  and 
may~eontinue  for  several  days,  as  is  the  case  with  the  Per- 
seids,  which  appear  in  early  August.  On  the  other  hand, 
the  flock  may  be  concentrated,  and  then  the  shower  will  occur 
only  when  the  earth  and  the  meteor  swarm  both  arrive  at  the 
orbit-crossing  together.  This  is  the  case  with  both  the  Leo- 
nids and  the  Andromedes.  The  showers  then  occur  not  every 
year,  but  only  at  intervals  of  several  years,  though  always  on 
or  near  the  same  day  of  the  month.  For  the  Leonids,  the 
interval  is  about  thirty-three  years,  and  for  the  Bielids  about 
thirteen  years. 

326.  The  meteors  which  belong  to  the  same  group  have  a 
marked   family  resemblance.     The   Perseids  are  yellow,  and 


§  326]  COMETS   AND  METEORS.  239 

move  with,  medium  velocity.  The  Leonids  are  very  swift  (we 
meet  them),  and  they  are  of  a  bluish  green  tint,  with  vivid 
trains.  The  Bielids  are  sluggish  (they  overtake  the  earth), 
are  reddish,  being  less  intensely  heated  than  the  others,  and 
they  usually  have  only  feeble  trains.  During  these  showers 
no  sound  is  heard,  no  sensible  heat  perceived,  nor  do  any 
masses  of  matter  reach  the  ground :  with  one  exception,  how- 
ever, that  on  Nov.  27th,  1885,  a  piece  of  meteoric  iron  fell  at 
Mazapil,  in  Northern  Mexico,  during  the  shower  of  Androme- 
des,  which  occurred  that  evening.  The  coincidence  may  be 
accidental,  but  is  certainly  interesting.  Many  high  author- 
ities speak  confidently  of  this  piece  of  iron  as  a  piece  of  Biela's 
comet  itself ;  and  this  brings  us  to  one  of  the  most  important 
astronomical  discoveries  of  the  last  half-century. 

327.  The  Connection  between  Comets  and  Meteors.  —  At  the 

time  of  the  great  meteoric  shower  of  1883,  Professors  Olmsted 
and  Twining  of  New  Haven  were  the  first  to  recognize  the 
"  radiant,"  and  to  point  out  its  significance  as  indicating  that 
the  meteors  must  be  members  of  a  swarm  of  bodies  revolving 
around  the  sun  in  a  permanent  orbit.  In  1864  Professor 
Newton  of  New  Haven,  taking  up  the  subject  anew,  showed 
by  an  examination  of  the  old  records  that  there  had  been  a 
number  of  great  meteoric  showers  about  the  middle  of  Novem- 
ber at  intervals  of  thirty-three  or  thirty-four  years  j  and  he 
predicted  confidently  the  repetition  of  the  shower  on  Nov. 
13th  or  14th,  1866.  It  occurred  as  predicted,  and  was  ob- 
served in  Europe ;  and  it  was  followed  by  another,  in  1867, 
which  was  visible  in  America,  the  meteoric  swarm  being  ex- 
tended in  so  long  a  procession  as  to  require  more  than  two 
years  to  cross  the  earth's  orbit.  The  researches  of  Newton 
and  Adams  showed  that  the  flock  was  moving  in  a  long  ellipse 
with  a  period  of  thirty-three  years. 

328.  Identification    of    Meteoric    and    Cometary    Orbits. — 

Within  a  few  weeks  after  the  shower  of  1866  it  was  found 


240 


ORBITS   OF  METEORIC   SWARMS. 


[§328 


that  the  orbit  pursued  by  these  meteors  was  identical  with 
that  of  a  comet,  known  as  Tempel's,  which  had  been  visible 
about  a  year  before;  and  about  the  same  time  Schiaparelli 
showed  that  the  Perseids,  or  August  meteors,  move  in  an  orbit 
identical  with  that  of  the  bright  comet  of  1862.  Now  a  single 
coincidence  might  be  accidental,  but  hardly  two.  Five  years 
later  came  the  shower  of  Andromedes,  following  in  the  track 
of  Biela's  comet ;  and  among  the  more  than  a  hundred  distinct 


FIG.  69.  —  Orbits  of  Meteoric  Swarms. 

meteor  swarms  now  recognized,  Professor  Alexander  Herschel 
finds  five  others  which  are  similarly  related,  each  to  its  special 
comet.  It  is  no  longer  possible  to  doubt  that  there  is  a  real 
and  close  connection  between  these  comets  and  their  attend- 
ant meteors.  Fig.  69  represents  four  of  the  orbits  of  these 
cometo-meteoric  bodies. 

329.   Nature  of  the  Connection.  —  This  cannot  be  said  to  be 
ascertained.     In  the  case  of  the*  Leonids  and  Andromedes,  the 


329] 


ORIGIN   OF  THE  LEONIDS. 


241 


meteoric  swarm  follows  the  comet,  but  this  does  not  seem  to 
be  so  in  the  case  of  the  Perseids,  which  scatter  along  more  or 
less  abundantly  every  year.  The  prevailing  belief  is  that  the 
comet  itself  is  only  the  thickest  part  of  the  meteoric  swarm, 
and  that  the  clouds  of  meteors  scattered  along  its  path  are  the 
result  of  its  disintegration;  but  this  is  by  no  means  certain. 

It  is  easy  to  show  that  if  the  comet  really  is  such  a  swarm,  it  must 
at  each  return  to  perihelion  gradually  break  up  more  and  more,  and  dis- 
perse its  constituent  particles  along  its  path,  until  the  compact  swarm 
has  become  a  diffuse  ring.  The  longer  the  comet  has  been  moving 


FIG.  70.  —  Origin  of  the  Leonids. 

around  the  sun,  the  more  uniformly  the  particles  will  be  distributed. 
The  Perseids,  therefore,  are  supposed  to  have  been  in  the  system  for  a 
long  time,  while  the  Leonids  and  Andromedes  are  believed  to  be  com- 
paratively new  comers.  Leverrier,  indeed,  has  gone  so  far  as  to  indicate 
the  year  126  B.C.  as  the  time  at  which  Uranus  captured  Tempel's 
comet,  and  brought  it  into  the  system,  as  illustrated  by  Fig.  70.  But 
the  theory  that  meteoric  swarms  are  the  product  of  cometary  disinte- 
gration assumes  the  premise  that  comets  enter  the  system  as  compact 
clouds,  which,  to  say  the  least,  is  not  yet  certain. 


242         MR.  LOCKYER'S  METEORIC  HYPOTHESIS.        t§  330 

330.  Mr.  Lockyer's  Meteoric  Hypothesis.  —  Within  the  last 
few  years  Mr.  Lockyer  has  been  enlarging  the  astronomical  impor- 
tance of  meteors.  The  probable  meteoric  constitution  of  the  zodiacal 
light,  as  well  as  of  Saturn's  rings,  and  of  the  comets,  has  long  been 
recognized;  but  he  goes  much  farther,  and  maintains  that  all  the 
heavenly  bodies  are  either  meteoric  swarms,  more  or  less  condensed, 
or  the  final  products  of  such  condensation  ;  and  upon  this  hypothesis 
he  attempts  to  explain  the  evolution  of  the  planetary  system,  the 
phenomena  of  variable  and  colored  stars,  the  various  classes  of  stellar 
spectra,  and  the  forms  and  structure  of  the  nebulse,  —  indeed  pretty 
much  everything  in  the  heavens  from  the  Aurora  Borealis  to  the  sun. 
As  a  "  working  hypothesis,"  his  theory  is  unquestionably  important, 
and  has  attracted  much  attention,  but  it  does  not  bear  criticism  in  all 
its  details. 


331]  THE   STARS.  243 


CHAPTER  XL 

THE  STARS. 

THEIR  NATURE,  NUMBER,  AND  DESIGNATION.  —  STAR 
CATALOGUES  AND  CHARTS.  —  PROPER  MOTIONS  AND 
THE  MOTION  OF  THE  SUN  IN  SPACE.  —  STELLAR  PAR- 
ALLAX. —  STAR  MAGNITUDES.  —  VARIABLE  STARS.  — 
STELLAR  SPECTRA. 

331.  THE  solar  system  is  surrounded  by  an  immense  void 
peopled  only  by  stray  meteors.     The  nearest  star,  as  far  as 
our  present  knowledge  goes,  is  one  whose  distance   is   more 
than  200,000  times  as  great  as  our  distance  from  the  sun,  — 
so  remote  that  from  it  the  sun  would  look  no  brighter  than 
the  Pole-star,  and  no  telescope  yet  constructed  would  be  able 
to  show  a  single  one  of  all  the  planets.     As  to  the  nature  of 
the  stars,  their  spectra  indicate  that  they  are  bodies  resem- 
bling our  sun,  —  that  is,  incandescent,  and  each  shining  with 
its  own  peculiar  light.     Some  are  larger  and  hotter  than  the 
sun,   others    smaller   and  cooler;    some,   perhaps,   large   but 
hardly  luminous  at  all.     They  differ  enormously  among  them- 
selves, not  being,  as  once  thought,  as  much  alike  as  individuals 
of  the  same  race,  but  differing  as  widely  as  animalcules  from 
elephants. 

332.  Number  of  Stars.  —  Those  which  are  visible  to  the  eye, 
though  numerous,  are  by  no  means  countless.     If  we  take  a 
limited  region,  for  instance,  the  bowl  of  the  Dipper,  we  shall 
find  that  the  number  we  can  see  within  it  is  not  very  large,  — 


244  NUMBER   OF   STABS.  [§  332 

hardly  a  dozen.  In  the  whole  celestial  sphere,  the  number  of 
stars  bright  enough  to  be  distinctly  seen  by  an  average  eye  is 
only  between  6000  and-  7000,  even  in  a  perfectly  clear  and 
moonless  sky;  a  little  haze  or  moonlight  will  cut  down  the 
number  fully  one-half.  At  any  one  time  not  more  than  2000 
or  2500  are  fairly  visible,  since  near  the  horizon  the  small  stars 
(which  are  vastly  the  more  numerous)  all  disappear.  The 
total  number  which  could  be  seen  by  the  ancient  astronomers 
well  enough  to  be  observable  with  their  instruments  is  not 
quite  1100.  With  even  the  smallest  telescope,  however,  the 
number  is  enormously  increased.  A  common  opera-glass 
brings  out  at  least  100,000,  and  with  a  2-J-  inch  telescope  Arge- 
lander  made  his  "  Durchmusterung "  of  the  stars  north  of  the 
equator,  more  than  300,000  in  number.  The  Lick  telescope, 
36  inches  in  diameter,  probably  makes  visible  at  least 
100,000/)00. 

333.  Constellations.  —  The   stars  are  grouped  in  so-called 
"constellations,"  many  of  which  are  extremely  ancient.     All 
of  those  of  the  zodiac  and  most  of  those  near  the  north  pole 
antedate  history.     Their  names  are,  for  the  most  part,  drawn 
from  the  Greek  and  Roman  mythology,  many  of  them  being 
connected  in  some  way  or  other  with  the  Argonautic  Expedi- 
tion.   In  some  cases  the  eye,  with  the  help  of  a  lively  imagi- 
nation, can  trace  in  the  arrangement  of  the   stars  a  vague 
resemblance  to  the  object  which  gives  the  name  to  the  constel- 
lation ;  but  generally  no  reason  is  obvious  for  either  name  or 
boundaries. 

We  have  already,  in  Chapter  II.,  given  a  brief  description 
of  those  constellations  which  are  visible  in  the  United  States, 
with  maps  and  directions  for  tracing  them. 

334.  Designation  of  the  Stars.  —  In  Art.  24  we  have  already 
indicated  the  different  methods  by  which  the  brighter  stars 
are  designated,  —  by  proper  names,  position  in  the  constellation, 


§  334]  STAB-CATALOGUES.  245 

or  by  letters  of  the  Greek  and  Eoman  alphabets.  But  these 
methods  do  not  apply  to  the  telescopic  stars,  at  least  to  any 
considerable  extent.  Such  stars  we  identify  by  their  cata- 
logue number ;  that  is,  we  refer  to  them  as  No.  so-and-so  in 
some  one's  star-catalogue.  Thus  LI.,  21,185  is  read  "  Lalande, 
21,185,"  and  means  the  star  that  is  so  numbered  in  Lalande's 
catalogue.  At  present  not  far  from  800,000  stars  are  cata- 
logued, so  that,  except  in  the  Milky  Way,  every  star  visible 
in  a  three-inch  telescope  can  be  found  and  identified.  Of 
course  all  the  bright  stars  which  have  names,  have  letters  also, 
and  are  sure  to  be  found  in  every  catalogue  which  covers  their 
part  of  the  heavens.  A  conspicuous  star,  therefore,  has  usu- 
ally many  "  aliases,"  and  sometimes  great  care  is  necessary  to 
avoid  mistakes  on  this  account. 

335.  Star-catalogues  are  carefully  arranged  lists  of  stars, 
giving  their  positions  (i.e.,  their  right  ascensions  and  declina- 
tions, or  latitudes  and  longitudes)  for  a  given  date,  and  usually 
also  indicating  their  so-called  magnitudes  or  brightness.  The 
earliest  of  these  star-catalogues  was  made  about  125  B.C.  by 
Hipparchus  of  Bithynia,  the  first  of  the  world's  great  astrono- 
mers, and  gives  the  latitudes  and  longitudes  of  1080  stars. 
This  catalogue  was  republished  by  Ptolemy  250  years  later, 
the  longitudes  being  corrected  for  precession  ;  and  during  the 
Middle  Ages  several  other  catalogues  were  made  by  Arabic 
astronomers  and  those  that  followed  them.  The  modern  cata- 
logues are  numerous ;  some,  like  Argelander's  "  Durchmuster- 
ung,"  give  the  places  of  a  great  number  of  stars  rather  roughly, 
merely  as  a  means  of  ready  identification.  Others  are  "  cata- 
logues of  precision,"  like  the  Pulkowa  and  Greenwich  cata- 
logues, which  give  the  places  of  only  a  few  hundred  so-called 
"fundamental"  stars,  determined  as  accurately  as  possible, 
each  star  by  itself.  Finally,  we  have  the  so-called  "zones," 
which  give  the  place  of  many  thousands  of  stars,  determined 
accurately  but  not  independently ;  that  is,  their  positions  are 


246         STAB-CHARTS  AND   STELLAR   PHOTOGRAPHY.      [§  335 

determined  by  reference  to  the  fundamental  stars  in  the  same 
region  of  the  sky. 

336.  Mean  and  Apparent  Places  of  the  Stars.  —  The  mod- 
ern star-catalogue  contains  the  mean  right  ascension  and  declination 
of  its  stars  at  the  beginning  of  some  designated  year ;  i.e.,  the  place 
the  star  would  occupy  if  there  were  no  nutation,  or  aberration  (Art. 
126,  and  Appendix,  435).     To  get  the  actual  (apparent)  right  ascen- 
sion and  declination  of  a  star  for  some  given  date,  which  is  what  we 
always  want  in  practice,  the  catalogue  place  must  be  "reduced"  to 
that  date;  i.e.,  it  must  be  corrected  for  precession,  etc.     The  opera- 
tion is  an  easy  one  with  modern  tables  and  formulae,  but  tedious  when 
many  stars  are  in  question. 

337.  Star-charts  and  Stellar  Photography. — For  some  pur- 
poses, accurate   star-charts  are  even   more  useful  than  cata- 
logues.    The  old-fashioned  and  laborious  way  of  making  such 
charts  was  by  "plotting"  the  results  of  zone  observations,  but 
at  present  it  is  being  done  by  means  of  photography,  vastly 
better  and  more  rapidly.     A  co-operative  international  cam- 
paign is  now  in  progress,  the  object  of  which  is  to  secure  a 
photographic  chart  of  all  the  stars  down  to  the  14th  magni- 
tude.    The  work  is  expected  to  occupy  a  dozen  instruments  in 
different  countries  for  the  next  six  or  seven  years.     One  of 
the  most  remarkable  things  about  the  photographic  method  is 
that  there  appears  to  be  no  limit  to  the  faintness  of  the  stars 
that  can  be  photographed  with  a  good  instrument.     By  in- 
creasing the  time  of  exposure,  smaller  and  smaller  stars  are 
continually  reached.     With  the  ordinary  plates  and  exposure- 
times  not  exceeding  twenty  minutes,  it  is  now  possible  to  get 
distinct  photographs  of  stars  that  the  eye  cannot  possibly  see 
with  the  same  telescope. 

Fig.  71  represents  the  photographic  telescope  (fourteen 
inches  diameter,  and  eleven  feet  focus,  of  the  Paris  observa- 
tory). The  other  instruments  engaged  in  the  star-chart  cam- 
paign are  substantially  like  it,  though  differing  more  or  less 
in  minor  details. 


338]  STELLAR    PHOTOGRAPHY.  247 


FIG.  71.  — Photographic  Telescope  of  the  Paris  Observatory. 


248  STAR   MOTIONS.  [§337 

Professor  Pickering  of  Cambridge,  U.S.,  is  also  planning  an  inde- 
pendent work  of  the  same  kind,  with  an  instrument  which  is  to  have 
a  four-lens  object-glass  of  twenty-four  inches  diameter  and  eleven  feet 
focus.  It  will  take  much  larger  plates  and  require  much  shorter 
exposures  than  the  Paris  instrument,  and  so  will  do  the  work  much 
more  rapidly.  It  is  intended  to  erect  it  upon  some  mountain,  first  in 
the  northern  hemisphere  and  then  in  the  southern. 

STAR   MOTIONS. 

338.  The  stars  are  ordinarily  called  "  fixed/'  in  distinction 
from  the  planets,  or  "wanderers/'  because  they  keep  their 
positions  and  configurations  sensibly  unchanged  with  respect 
to  each  other  for  long  periods  of  time.     Delicate  observations, 
however,  demonstrate  that  the  fixity  is  not  absolute,  but  that 
the  stars  are  really  in  motion.     Moreover,  by  the  spectroscope 
their  rate  of  motion  towards  or  from  the  earth  can  in  some 
cases  be  approximately  measured.    In  fact,  it  appears  that  the 
velocities  of  the  stars  are  of  the  same  order  as  those  of  the 
planets.     The  stars  are  flying  through  space  far  more  swiftly 
than  cannon-balls,  and  it  is  only  because  of  their  enormous  dis- 
tance from  us  that  they  appear  to  change  their  positions  so 
slowly. 

339.  Proper    Motion.  —  If    we  compare  a  star's    position 
(right  ascension  and  declination)  as  determined  to-day  with 
that  observed  100  years  ago,  it  will  always  be  found  to  have 
changed  considerably.     The  difference  is  due  in  the  main  to 
precession  (Art.  125)  ;  but  after  allowing  for  all  such  merely 
apparent  motions  of  a  star,  it  generally  turns  out  that  within  a 
century  the  star  has  really  altered  its  place  more  or  less  with 
reference  to  others  near  it,  and  this  real  shifting  of  its  place  is 
called  its  "  proper  motion."     Of  two  stars  side  by  side  in  the 
same   telescopic  field  of  view,  the  proper  motions   may  be 
directly  opposite,  while,  of  course,  the  apparent  motions  (due 
to  precession,  etc.)  will  be  sensibly  the  same. 


VELOCITY   OF   STAR   MOTIONS.  249 

Even  the  largest  of  these  proper  motions  is  very  small. 
The  largest  at  present  known,  that  of  the  so-called  "  run-away 
star,"  1830  Groombridge,  is  only  7"  a  year.  (This  star  is  not 
visible  to  the  naked  eye.)  About  a  dozen  stars  are  known  to 
have  an  annual  proper  motion  exceeding  3",  and  about  150,  so 
far  as  known  at  present,  exceed  1".  The  proper  motions  of 
the  bright  stars  average  higher  than  those  of  the  faint,  as 
might  be  expected,  since  on  the  average  the  bright  ones  are 
probably  nearer.  For  the  first-magnitude  stars,  the  average  is 
about  J"  annually;  and  for  the  sixth-magnitude  stars,  the 
smallest  visible  to  the  naked  eye,  it  appears  to  be  about  ^". 

Motions  of  this  kind  were  first  detected  in  1718  by  Halley,  who 
found  that  since  the  time  of  Hipparchus  the  star  Arcturus  had  moved 
towards  the  south  nearly  a  whole  degree,  and  Sirius  about  half  as 
much. 

340.  Velocity  of  Star  Motions.  —  The  proper  motion  of  a 
star  gives  us  very  little  knowledge  as  to  the  star's  real  motion 
in  miles  per  second.  The  proper  motion  derived  from  the 
comparison  of  star-catalogues  of  different  dates  is  only  the 
value  in  seconds  of  arc  of  that  part  of  its  whole  motion  which 
is  perpendicular  to  the  line  of  sight.  A  star  moving  straight 
towards  us  or  from  us  has  no  proper  motion  at  all ;  i.e.,  no 
change  of  apparent  place  which  can  be  detected  by  comparing 
observations  of  its  position. 

We  can,  however,  in  some  cases  fix  a  minor  limit  to  the 
velocity  of  a  star.  We  know,  for  instance,  that  the  distance 
of  the  star,  1830  Groombridge,  is  certainly  not  less  than 
2,000000  '  astronomical  units/  and,  therefore,  since  its  yearly 
path  subtends  an  angle  of  7"  at  the  earth,  the  length  of  the 
path  must  at  least  equal  sixty-nine  astronomical  units  a  year, 
which  corresponds  to  a  velocity  of  over  200  miles  a  second. 
The  real  velocity  must  be  more  than  this,  but  how  much 
greater  we  cannot  determine  until  we  know  how  much  the 
star's  distance  exceeds  2,000000  units,  and  how  fast  it  is  mov- 
ing towards  or  from  us. 


250  MOTION   IN  THE  LINE   OF   SIGHT.  [§  340 

In  many  cases  a  number  of  stars  in  the  same  region  of  the 
sky  have  a  motion  practically  identical,  making  it  almost  cer- 
tain that  they  are  real  neighbors  and  in  some  way  connected, 
—  probably  by  community  of  origin.  In  fact,  it  seems  to  be 
the  rule  rather  than  the  exception  that  stars  which  are  appar- 
ently near  each  other  are  real  comrades  j  they  show,  as  Miss 
Clerke  expresses  it,  a  distinctly  "  gregarious  "  tendency. 

341.  Motion  in  the  Line  of  Sight.  — Within  the  last  thirty 
years  a  method1  has  been  developed  by  which  any  swift 
motion  of  a  star,  directly  towards  or  from  us,  may  be  detected 
by  means  of  the  spectroscope. 

If  a  star  is  approaching  us,  the  lines  of  its  spectrum  will 
apparently  be  shifted  towards  the  violet,  according  to  Doppler's 
principle  (Art.  197),  and  vice  versa,  if  it  is  receding  from  us. 
Visual  observations  of  this  sort,  first  made  by  Huggins  in 
1868,  and  since  then  by  many  others,  have  succeeded  in  dem- 
onstrating the  reality  of  these  motions  in  the  line  of  sight 
and  in  roughly  measuring  some  of  them.  Recently  Vogel  of 
Potsdam  has  taken  up  the  investigation  photographically,  and 
has  obtained  results  that  are  far  more  satisfactory  than  any 
before  reached.  He  photographs  the  spectrum  of  the  star  and 
the  spectrum  of  hydrogen  gas,  or  some  other  substance  whose 
lines  appear  in  the  star  spectrum,  together  upon  the  same 
plate,  the  light  from  both  being  admitted  through  the  same 
slit.  If  the  star  is  not  moving  towards  or  from  us,  its  lines 
will  coincide  precisely  with  those  of  the  comparison  spectrum ; 
otherwise,  they  will  deviate  one  way  or  the  other. 

1  It  is  not,  as  students  sometimes  think,  by  changes  in  the  apparent 
size  and  brightness  of  a  star.  Theoretically,  of  course,  a  star  which  is 
approaching  us  must  grow  brighter,  but  even  the  nearest  star  of  all,  Alpha 
Centauri  (Art.  343)  is  so  far  away  that  if  it  were  coming  directly  towards 
us  at  the  rate  of  100  miles  a  second,  it  would  require  more  than  8000  years 
to  make  the  journey ;  so  that  in  a  century  its  brightness  would  only 
change  about  two  per  cent,  —  far  too  little  to  be  observed. 


§  341]  THE  SUN'S   WAY.  251 

Fig.  72  is  from  one  of  his  negatives  of  the  spectrum  of  Beta  Orionis 
(Rigel),  in  which  one  of  its  dark  lines  is  compared  with  the  corre- 
sponding bright  lines  in  the  spectrum 

of  hydrogen.      The  dark  line  of  the    Blue  |  Red 

stellar  spectrum  (bright  in  the  nega- 
tive) is  shifted  towards  the  red  by  an 
amount  which  indicates  that  at  the  Spectrum  of  Rigel 

time  the  star  was  rapidly  receding.  ^  72.  _  Di8placement  of  Hy  Line 

For  the  most  part,  these  motions        in  the  Spectrum  °f '  °rioni8' 
of  the  stars,  so  far  as  ascertained,  seem  to  range  between  zero 
and  fifty  miles  a  second,  with  still  higher  speeds  in  a  few 
exceptional  cases. 


342.  The  "Sun's  Way."  —  The  proper  motions  of  the  stars 
are  due  partly  to  their  own  real  motions,  but  partly  also  to  the 
motion  of  the  sun,  which,  like  the  other  stars,  is  travelling 
through  space,  taking  with  it  its  planets.  Sir  William  Her- 
schel  was  the  first  to  investigate  and  determine  the  direction 
of  this  motion  a  century  ago.  The  principle  involved  is  this  : 
On  the  whole  the  stars  appear  to  drift  bodily  in  a  direction 
opposite  to  the  sun's  real  motion.  Those  in  that  quarter  of 
the  sky  which  we  are  approaching  open  out  from  each  other, 
and  those  in  the  rear  close  up  behind  us.  The  motions  of  the 
individual  stars  lie  in  all  possible  directions,  but  when  we 
deal  with  them  by  thousands,  the  individual  is  lost  in  the 
general,  and  the  prevailing  drift  appears. 

About  twenty  different  determinations  of  the  point,  towards 
which  the  sun's  motion  is  directed,  have  been  made  by  various 
astronomers.  There  is  a  reasonable  and  almost  surprising 
accordance  of  results,  and  they  all  show  that  the  sun  is  mov- 
ing towards  a  point  in  the  constellation  of  Hercules,  having  a 
right  ascension  of  about  267°  (17h  48m),  and  a  declination  of 
about  32°  north.  This  point  is  called  the  "  apex  of  the  sun's 
way."  As  to  the  velocity  of  this  motion  of  the  sun,  it  comes 
out  as  about  0".05  annually,  seen  from  the  average  distance  of 


252  PARALLAX  OF  A  STAR.  [§  342 

the  standard  sixth-magnitude  star.  It  is  assumed  by  high 
authorities,  on  grounds  that  we  cannot  stop  to  discuss,  that 
this  distance  is  about  20,000000  astronomical  units;  and  on 
that  assumption,  the  speed  of  the  sun's  motion  is  about  sixteen 
miles  a  second.  But  the  result  is  to  be  taken  as  hardly  more 
than  a  reasonable  guess. 

THE  PARALLAX  AND  DISTANCE  OF  STARS. 

343.  When  we  speak  of  the  "  parallax "  of  the  sun,  of  the 
moon,  or  of  a  planet,  we  always  mean  the  "  diurnal "  or  "  geo- 
centric "  parallax  (Art.  139) ;  i.e.,  the  apparent  semi-diameter 
of  the  earth  as  seen  from  the  body.  In  the  case  of  a  star,  this 
kind  of  parallax  is  practically  nothing,  never  reaching  ^-J-^-g- 
of  a  second  of  arc.  The  expression,  "parallax  of  a  star," 
always  refers,  on  the  contrary,  to  its  "annual"  or  "helio- 

E 

PIG.  73.  — The  Annual  Parallax  of  a  Star. 

centric  "  parallax ;  i.e.,  the  apparent  semi-diameter,  not  of  the 
earth,  but  of  the  earth's  orbit,  as  seen  from  the  star.  In 
Fig.  73  the  angle  at  the  star  is  its  parallax. 

Even  this  heliocentric  parallax,  in  the  case  of  most  stars,  is 
far  too  small  to  be  detected  by  our  present  instruments :  it 
never  reaches  a  single  second  of  arc.  But  in  a  few  instances 
it  has  been  actually  measured.  Alpha  Centauri,  which  is  our 
nearest  neighbor,  so  far  as  yet  known,  has  a  parallax  of  about 
0".9,  according  to  the  earlier  observers,  or  only  0".T5,  accord- 
ing to  the  latest  authorities.  There  are  but  four  or  five  other 
stars  at  present  known  which  have  a  parallax  more  than  half 
as  great  as  this.  (For  the  method  of  determining  stellar 
parallax,  see  Appendix,  Arts.  441-443.) 


§344]  THE  LIGHT-YEAB.  253 

344.  Unit  of  Stellar  Distance;  the  Light-year.  —  The  dis- 
tances of  the  stars  are  so  enormous  that  even  the  radius  of 
the  earth's  orbit,  the  "  astronomical  unit "  hitherto  employed, 
is  far  too  small  for  convenience.     It  is  better,  and  now  usual, 
to  take  as  the  unit  of  stellar  distance  the  so-called  light-year; 
i.e.,  the  distance  which  light  travels  in  a  year.     This  is  about 
63,000  times  the  distance  of  the  earth  from  the  sun. 

This  number  is  found  by  dividing  the  number  of  seconds  in  a  year 
by  499,  the  number  of  seconds  required  by  light  to  make  the  journey 
from  the  sun  to  the  earth  (Appendix,  Art.  432). 

A  star  with  a  parallax  of  1"  is  at  a  distance  of  3.26  light- 

O    O£J 

years,  and  in  general  the  distance  in  light-years  equals  -^y-, 

where  p"  is  the  parallax  of  the  star  expressed  in  seconds. 

So  far  as  can  be  judged  from  the  scanty  data,  it  appears 
that  few  if  any  stars  are  nearer  than  four  light-years  from  the 
solar  system ;  that  the  naked-eye  stars  are  probably,  for  the 
most  part,  within  200  or  300  years ;  and  that  many  of  the  re- 
moter stars  must  be  thousands,  or  even  tens  of  thousands,  of 
light-years  away. 

For  the  parallaxes  of  a  number  of  stars,  see  Table  V., 
Appendix. 

THE   LIGHT  OF  THE   STARS. 

345.  Star  Magnitudes.  —  As  has   already  been  mentioned 
(Art.  23),  Hipparchus   and  Ptolemy  arbitrarily  divided   the 
stars   into   six   "magnitudes"  according  to  their  brightness, 
the  stars  of  the  sixth  magnitude  being  those  which  are  barely 
perceptible  by  an  ordinary  eye,  while  the  first  class  comprise 
about  twenty  of  the  brightest.     After  the  invention  of  the 
telescope  the  same  system  was  extended  to  the  smaller  stars, 
though  without  any  special  plan,  so  that  the  "magnitudes" 
assigned  to  telescopic   stars  by  different  observers  are  very 
discordant. 


254  SCALE   OF   STAR  MAGNITUDES.  [§345 

Heis  enumerates  the  stars  clearly  visible  to  the  naked  eye,  north  of 
the  35th  parallel  of  south  declination,  as  follows :  — 

First  Magnitude,  14.  Fourth  Magnitude,  313. 

Second         "         48.  Fifth  «          854. 

Third  "       152.  Sixth  «        2010. 

Total,  3391. 

It  will  be  noticed  how  rapidly  the  numbers  increase  for  the  smaller 
magnitudes.  Nearly  the  same  holds  good  also  for  the  telescopic  stars, 
though  below  the  tenth  magnitude  the  rate  of  increase  falls  off. 

346.   Light-ratio  and  "Absolute  Scale"  of  Star  Magnitudes. 

—  The  scale  of  magnitudes  ought  to  be  such  that  the  "light- 
ratio,"  or  number  of  times  by  which  the  brightness  of  any 
star  exceeds  that  of  a  star  which  is  one  magnitude  smaller, 
should  be  the  same  throughout  the  whole  extent  of  the  scale. 
This  relation  was  roughly,  but  not  accurately,  observed  by  the 
older  astronomers,  and  very  recently  Professor  Pickering  of 
Cambridge,  U.  S.,  and  Professor  Pritchard  of  Oxford,  England, 
have  made  photometric  measurements  of  the  brightness  of  all 
the  naked-eye  stars  visible  in  our  latitude,  and  have  re-classified 
them  according  to  the  so-called  "  absolute  scale,"  which  uses 
a  light-ratio  equal  to  the  fifth  root  of  100,  (2.51) ;  i.e.,  upon 
this  scale  a  star  of  the  third  magnitude  is  just  2.51  times 
brighter  than  one  of  the  fourth. 

This  ratio  is  based  upon  an  old  determination  of  Sir  John  Her- 
schel's,  who  found  that  the  average  first-magnitude  star  is  just  about 
a  hundred  times  as  bright  as  a  star  of  the  sixth  magnitude,  five  mag- 
nitudes fainter. 

On  this  scale,  Altair  (Alpha  Aquilse)  and  Aldebaran  (Alpha 
Tauri)  may  be  taken  as  standard  first-magnitude  stars,  while 
the  Pole-star  and  the  two  pointers  are  very  nearly  of  the  stand- 
ard second  magnitude. 

Of  course,  in  indicating  the  brightness  of  stars  with  precision,  frac- 
tional numbers  must  be  used ;  that  is,  we  have  stars  of  2.4  magni- 
tude, etc. 


§  346]         STARLIGHT   COMPARED   WITH   SUNLIGHT.  255 

Stars  that  are  brighter  than  Aldebaran  or  Altair  have  their  bright- 
ness denoted  by  a,  fraction,  or  even  by  a  negative  number;  thus  the 
absolute  magnitude  of  Vega  is  0.2,  and  of  Sirius  —  1.4.  The  necessity 
of  these  negative  and  fractional  magnitudes  for  bright  stars  is  rather 
unfortunate,  but  not  really  of  much  importance. 

347.  Magnitudes  and  Telescopic  Power.  —  If  a  good  telescope 
just  shows  a  star  of  a  certain  magnitude,  we  must  have  a  telescope 
with  its  aperture  larger  in  the  ratio  of  1.58  :  1,  in  order  to  show  stars 
one  magnitude  smaller;  (1.58=  V2.51).      A  tenfold  increase  in  the 
diameter  of  an  object-glass  theoretically  carries  the  power  of  vision 
just  five  magnitudes  lower. 

It  is  usually  estimated  that  the  12th  magnitude  is  the  limit  of  vision 
for  a  4-inch  glass.  It  would  require,  therefore,  a  40-inch  glass  to  reach 
the  17th  magnitude  of  the  absolute  scale. 

Our  space  does  not  permit  any  extended  discussion  of  the  methods 
by  which  the  brightness  of  stars  is  measured,  a  subject  which  has  of 
late  attracted  much  attention  (see  General  Astronomy,  Arts.  823-829). 

348.  Starlight    compared    with    Sunlight.  —  Zollner    and 
others  have  endeavored  to  determine  the  amount  of  light  l  re- 
ceived by  us  from  certain  stars,  as  compared  with  the  light  of 
the  sun.     According  to  him,  Sirius  gives  us  about  yinrrwffTJUiF 
as  much  light  as  the  sun  does,  and  Capella  and  Vega  about 

^  ^n^s  rate>  the  standard  first-magnitude  star, 


like  Altair,  should  give  us  about  sinnnroooooo?  and  ^  would 
take,  therefore,  about  nine  million  million  stars  of  the  sixth 
magnitude  to  equal  the  sun.  These  numbers,  however,  are 
very  uncertain.  The  various  determinations  for  Vega  vary 
more  than  fifty  per  cent. 

Assuming  what  is  roughly  true,  that  Argelander's  magnitudes  agree 
with  the  absolute  scale,  it  appears  that  the  324,000  stars  of  his  "  Durch- 

1  Undoubtedly,  the  stars  send  us  heat  also,  and  attempts  have  been 
made  to  measure  it  ;  but  there  is  no  reason  for  supposing  that  the  propor- 
tion of  stellar  heat  to  solar  differs  much  from  the  proportion  of  starlight  to 
sunlight  ;  and  if  so,  the  heat  of  a  star  must  be  far  below  the  possibility  of 
measurement  by  any  apparatus  yet  at  our  command. 


256  LIGHT  OF  CERTAIN  STABS.  [§  348 

musterung,"  all  of  them  north  of  the  celestial  equator,  give  a  light 
about  equivalent  to  240  or  250  first-magnitude  stars.  How  much 
light  is  given  by  stars  smaller  than  the  9|  magnitude  (which  was  his 
limit)  is  not  certain.  It  must  greatly  exceed  that  given  by  the  larger 
stars.  As  a  rough  guess  we  may  estimate  that  the  total  starlight  of 
both  the  northern  and  southern  hemispheres  is  equivalent  to  about 
3000  stars  like  Vega,  or  1500  at  any  one  time.  According  to  this,  the 
starlight  on  a  clear  night  is  about  ^  of  the  light  of  a  full  moon,  or 
about  ^j-jnhn^  that  of  sunlight.  More  than  95  per  cent  of  it  comes 
from  stars  which  are  entirely  invisible  to  the  naked  eye. 

349.  Amount  of  Light  emitted  by  Certain  Stars. — When 
we  know  the  distance  of  a  star  in  astronomical  units,  it  is  easy 
to  compute  the  amount  of  light  it  really  emits  as  compared 
with  that  given  off  by  the  sun.     It  is  only  necessary  to  mul- 
tiply the  light  we  now  get  from  it  (expressed  as  a  fraction  of 
sunlight)  by  the  square  of  the  star's  distance  in  astronomical 
units.     Thus,  the  distance  of  Sirius  is  about  550,000  units,  and 
the  light  we  receive  from  it  is  yooo  oooooo  °^  sunlight.     Mul- 
tiplying this  fraction  by  the  square  of  550,000,  we  find  that 
Sirius  is  really  radiating  more  than  forty  times  as  much  light 
as  the  sun.     As  for  several  other  stars,  whose  distance  and 
light  have  been  measured,  some  turn  out  brighter,  and  some 
darker  than  the  sun.     The  range  of  variation  is  very  wide, 
and  in  brilliance  the  sun  holds  apparently  about  a  medium 
rank  among  its  kindred. 

350.  Why  the  Stars   differ  in  Brightness.  —  The  apparent 
brightness  of  a  star,  as  seen  from  the  earth,  depends  both  on 
its  distance  and  on  the  quantity  of  light  it  emits,  and  the 
latter  depends  on  the  extent  of  its  luminous  surface  and  upon 
the  brightness  of  that  surface.     As  Bessel  long  ago  suggested, 
"  there  may  be  as  many  dark  stars  as  bright  ones."     Taken  as 
a  class,  the  bright  stars  undoubtedly  average  nearer  to  us  than 
the  fainter  ones,  and  just  as  undoubtedly  they  also  average 
larger  in  diameter  and  more  intensely  luminous ;  but  when  we 


§  350]  VARIABLE  STARS.  257 

compare  any  particular  bright  star  with  another  fainter  one, 
we  can  seldom  say  to  which  of  these  different  causes  it  owes 
its  superiority.  We  cannot  assert  that  the  faint  star  is  smaller 
or  darker  or  more  distant  than  that  particular  bright  star, 
unless  we  know  something  more  about  it  than  the  simple  fact 
that  it  is  fainter. 

351.  Dimensions  of  the  Stars.  —  The  stars  are  so  far  away 
that  their  apparent  diameters  are  altogether  too  small  to  be 
measured  by  any  known  form  of  micrometer.     The  sun  at  the 
distance  of  the  nearest  star  would  measure1  not  quite  0".01 
across.     Micrometers,  therefore,  do  not  help  us  in  the  matter, 
and  until  very  recently  we  were  absolutely  without  any  posi- 
tive knowledge  as  to  the  real  size  of  a  single  one  of  the  stars. 
But  in  1889,  by  a  spectroscopic  method,  more  fully  explained 
in  Art.  360,  Vogel  succeeded  in  showing  that  the  bright  vari- 
able star,  Algol  (Beta  Persei)  (Art.  358),  must  have  a  diam- 
eter of  about  1,160,000  miles,  while  its  invisible  companion  is 
about  840,000  miles  in  diameter,  or  just  about  the  size  of 
the  sun. 

VARIABLE   STARS. 

352.  Classes  of  Variables.  — Many  stars  are  found  to  change 
their  brightness  more  or  less,  and  are  known  as  "variable." 
They  may  be  classed  as  follows :  — 

I.   Stars  which  change   their  brightness  slowly  and   con- 
tinuously. 
II.   Those  that  fluctuate  irregularly. 

III.  Temporary  stars  which  blaze   out  suddenly  and  then 

disappear. 

IV.  Periodic  stars  of  the  type  of  "  Omicron  Ceti,"  usually 

having  a  period  of  several  months. 

1  This  does  not  refer,  of  course,  to  the  "  spurious  disc  "  of  the  star 
(Appendix,  Art.  408),  which  is  many  times  larger. 


258  GRADUAL  CHANGES.  [§  352 

V.   Periodic  stars  of  the  type  of  "  Beta  Lyrae,"  usually  hav- 
ing short  periods. 

VI.  Periodic  stars  of  the  "  Algol "  type,  in  which  the  period 
is  usually  short,  and  the  variation  is  like  what  might 
be  produced  if  the  star  were  periodically  "  eclipsed  " 
by  some  intervening  object. 

353.  Gradual  Changes.  —  The  number  of  stars  which  are 
certainly  known  to  be  gradually  changing  in  brightness  is  sur- 
prisingly small.     On  the  whole,  the  stars  present  not  only  in 
position,  but  in  brightness  also,  sensibly  the  same  relations  as 
in  the  catalogues  of  Hipparchus  and  Ptolemy. 

There  are,  however,  a  few  instances  in  which  it  can  hardly  be 
doubted  that  considerable  alteration  has  occurred  even  within  the  last 
two  or  three  centuries.  Thus,  in  1610  Bayer  lettered  Castor  as  Alpha 
Geminorum,  while  Pollux,  which  he  called  Beta  Geminorum,  is  now 
considerably  brighter.  There  are  about  a  dozen  other  similar  cases 
known,  and  a  much  larger  number  is  suspected. 

It  is  commonly  believed  that  a  considerable  number  of  stars  have 
disappeared  since  the  first  catalogues  were  made,  and  that  many  new 
ones  have  come  into  existence.  While  it  is  unsafe  to  deny  absolutely 
that  such  things  may  have  happened,  it  can  be  said,  on  the  other 
hand,  that  not  a  single  case  of  the  kind  is  certainly  known.  The  dis- 
crepancies between  the  older  and  newer  catalogues  are  all  accounted 
for  by  some  error  or  other  that  has  already  been  discovered. 

354.  Irregular  Fluctuations.  —  The  most  conspicuous  star 
of  the  second  class  is  Eta  Argus  (not  visible  in  the  United 
States).     It  varies  all  the  way  from  above  the  first  magnitude 
(in  1843  it  stood  next  to  Sirius)  down  to  the  seventh  magni- 
tude (invisible   to  the   eye),  which  has  been  its  status   ever 
since  1865,  though  recently  it  is  reported  as  slightly  brighten- 
ing up  again.     Alpha  Orionis  and  Alpha  Cassiopeise  behave  in 
a  similar  way,  except   that   their  variation  of  brightness  is 

small,  not  much  exceeding  half  a  magnitude. 


§  355]  TEMPORARY   STARS.  259 

355.  Temporary    Stars.  —  There   are   eleven   well-authenti- 
cated instances  of  stars  which  have  blazed  up  suddenly,  and 
then   gradually  faded  away  (see   General   Astronomy,   Arts. 
842-845).     The  most  remarkable  of  these  is  that  known  as 
Tycho's,  which   appeared   in   the   constellation  of  Cassiopeia 
(Art.  28)  in  November,  1572,  was  for  some  days  as  bright  as 
Venus  at  her  best,  and  then  gradually  faded  away,  until  at 
the  end  of  sixteen  months  it  became  invisible.     (There  were 
no  telescopes  then.)     It  is  not  certain  whether  it  still  exists  as 
a  telescopic  star:  so  far  as  we  can  judge  it  may  be  either  of 
half  a  dozen  which  are  near  the  place  determined  by  Tycho. 

There  has  been  a  curious  and  utterly  unfounded  notion  that  this 
star  was  the  "  Star  of  Bethlehem  "  and  would  reappear  to  herald  the 
second  advent. 

A  temporary  star  which  appeared  in  the  constellation  Corona 
Borealis,  in  May,  1866,  is  interesting  as  having  been  spectro- 
scopically  examined  when  near  its  brightest  (second  magni- 
tude). It  then  showed  the  same  bright  lines  of  hydrogen 
which  are  conspicuous  in  the  solar  prominences.  Before  its 
outburst  it  was  an  eighth-magnitude  star  of  Argelander's  cata- 
logue, and  within  a  few  months  it  returned  to  its  former  low 
estate,  which  it  still  retains. 

The  most  recent  instance  is  that  of  a  sixth-magnitude  star 
which  in  August,  1885,  suddenly  appeared  in  the  midst  of  the 
great  nebula  of  Andromeda  (Art.  377).  In  a  few  months  it 
totally  disappeared,  even  to  the  largest  telescopes. 

356.  Variables  of  the  "Omicron  Ceti"  Type.— These  ob- 
jects behave  almost  exactly  like  a  temporary  star  in  remain- 
ing most  of  the  time   faint,  suddenly  blazing  out,  and  then 
gradually  fading  away,  —  but  they  do  it  periodically.     Omicron 
Ceti,  or  Mira  (i.e.,  "  the  wonderful ")  is  the  type.     It  was  dis- 
covered in  1596,  and  was  the  first  variable  star  known.     Dur- 
ing most  of  the  time  it  is  of  the  ninth  magnitude,  but  at 
intervals  of  about   eleven  months  it  runs  up  to  the  fourth, 


260 


TYPES   OF   VARIABLE  STARS. 


[§356 


third,  or  even  second  magnitude,  and  then  back  again,  the 
whole  change  occupying  about  100  days,  and  the  rise  being 
much  more  rapid  than  the  fall.  It  remains  at  its  maximum 
about  a  week  or  ten  days.  The  maximum  brightness  varies 
very  considerably,  and  its  period,  while  always  about  eleven 


oCeti 
(Mira) 


Period  11  months  ± 


FIG.  74.  —  Light-curves  of  Variable  Stars. 

months,  varies  to  the  extent  of  two  or  three  weeks.  The 
spectrum  of  the  star  when  brightest  is  very  beautiful,  show- 
ing a  large  number  of  intensely  bright  lines,  some  of  which 
are  due  to  hydrogen.  Its  light-curve  is  A  in  Fig.  74. 

Nearly  half  of  all  the  known  variables  belong  to  this  class, 
and  a  large  proportion  of  them- have  periods  which  do  not 
differ  very  widely  from  a  year.  Most  of  the  periods,  how- 
ever, are  more  or  less  irregular.  Some  writers  include  the 
temporary  stars  in  this  class,  maintaining  that  the  only  differ- 
ence is  in  the  length  of  their  period. 

357.  Class  V.  — The  variables  of  Class  V.  are  mostly  of 
short  period,  and  are  characterized  by  a  continual  rising  and 


§  357]  EXPLANATION   OF  VARIABLE   STARS.  261 

falling  of  brightness,  running  through  the  whole  period. 
Sometimes  there  are  two,  or  even  three,  maxima  before  the 
cycle  is  completed.  The  light-curve  of  Beta  Lyrse,  the  type- 
star  of  this  class  (period  about  thirteen  days)  is  B  in  Fig.  74. 

358.  The  "Algol"   Type.  —  In  the  stars  of  Class  VI.  the 
variation  is  precisely  the  reverse  of  that  in  Class  IV.     The 
star  remains  bright  for  most  of  the  time,  but  apparently  suffers 
a  periodical  eclipse.     The   periods  are  mostly  very  short, — 
only  a  few  days,  —  and  one  little  star  in  the  constellation  of 
Antlia  has  a  period  of  less  than  eight  hours. 

Algol  (Beta  Persei)  is  the  type-star.  During  most  of  the 
time  it  is  of  the  second  magnitude,  and  it  loses  about  five- 
sixths  of  its  light  at  the  time  of  obscuration.  The  fall  of 
brightness  occupies  about  4£  hours.  The  minimum  lasts  about 
20  minutes,  and  the  recovery  of  light  takes  about  3£  hours. 
The  period,  a  little  less  than  three  days,  is  known  with  great 
precision,  to  a  single  second  indeed,  and  is  given  in  connec- 
tion with  the  light-curve  of  the  star  in  Fig.  74.  At  present 
the  period  seems  to  be  slowly  shortening.  Less  than  a  dozen 
stars  are  as  yet  known  in  this  class. 

359.  Explanation  of  Variable  Stars. — No  single  explana- 
tion will  cover  the  whole  ground.     As  to  progressive  changes, 
no  explanation  may  be  looked  for.     The  wonder  rather  is  that 
as  the  stars  grow  old,  such  changes  are  not  more  notable  than 
they  are. 

As  for  irregular  changes,  no  sure  account  can  yet  be  given. 
Where  the  range  of  variation  is  small  (as  it  is  in  most  cases), 
one  thinks  of  spots  upon  the  surface  of  the  star,  more  or  less 
like  sun  spots ;  and  if  we  suppose  these  spots  to  be  much  more 
extensive  and  numerous  than  are  the  sun  spots,  and  also,  like 
them,  to  have  a  regular  period  of  frequency,  and  also  that  the 
star  revolves  upon  its  axis,  we  find  in  the  combination  a  pos- 
sible explanation  of  a  large  proportion  of  all  the  variable  stars. 


262  EXPLANATION   OF   THE   ALGOL   TYPE.  [§359 

For  the  temporary  stars,  we  may  imagine  either  great  erup- 
tions of  glowing  matter,  like  solar  prominences  on  an  enor- 
mous scale,  or,  with  Mr.  Lockyer,  we  may  imagine  that  most 
of  the  variable  stars  are  only  swarms  of  meteors,  rather  com- 
pact, but  not  yet  having  reached  the  condensed  condition 
of  our  own  sun.  Stars  of  the  Mira  type,  according  to  this 
theory,  owe  their  regular  outbursts  of  brightness  to  the  collis- 
ions, due  to  the  passage  of  a  smaller  swarm  through  the  outer 
portions  of  a  larger  one,  around  which  the  smaller  is  supposed 
to  revolve  in  a  long  oval.  But  the  great  irregularity  in  the 
periods  of  variables  belonging  to  this  class  is  hard  to  recon- 
cile with  a  true  orbital  revolution,  which  usually  keeps  time 
accurately. 

360.  Explanation  of  the  Algol  Type.  —  The  natural  and 
most  probable  explanation  of  the  behavior  of  these  stars  is  that 
the  periodical  darkening  is  produced  by  the  interposition  of 
some  opaque  body  between  us  and  the  star.  This  eclipse  theory 
has  lately  received  a  striking  confirmation  from  the  spectro- 
scopic  work  of  Vogel,  who  has  found  by  the  method  indicated 
in  Art.  341  that  about  seventeen  hours  before  the  obscuration, 
Algol  is  receding  from  us  at  the  rate  of  nearly  twenty-seven 
miles  a  second,  while  seventeen  hours  after  the  minimum  it 
approaches  us  at  the  same  rate.  This  is  just  what  it  ought  to 
do,  if  it  had  a  large,  dark  companion,  and  the  two  were  revolv- 
ing around  their  common  centre  of  gravity  in  an  orbit  nearly 
edgewise  to  the  earth.  When  the  dark  star  is  rushing  for- 
ward to  interpose  itself  between  us  and  Algol,  Algol  itself 
must  be  moving  backwards,  and  vice  versa  when  the  dark  star 
is  receding  after  the  eclipse.  Vogel's  conclusions  are,  that  the 
distance  of  the  dark  star  from  Algol  is  about  3,250000  miles ; 
that  their  diameters  are  respectively  about  840,000  and 
1,160000  miles;  that  their  united  mass  is  about  two-thirds 
that  of  the  sun ;  and  their  density  about  one-fifth  that  of  the 
sun,  —  not  much  greater  than  that  of  cork. 


§361]  STAR    SPECTRA.  263 

361.  Number  and  Designation  of  Variables,  and  their  Range 
of  Variation.  —  Mr.  Chandlers  catalogue  of  known  variables, 
with  its  recent  supplement,  includes  238  objects,  and  there  is 
also  a  considerable  number  of  suspected  variables. 

169  of  the  238  are  distinctly  periodic.  The  rest  of  them  are 
some  irregular,  some  temporary,  and  in  respect  to  many  we 
have  not  yet  certain  knowledge  whether  the  variation  is  or  is 
not  periodic. 

Table  IV.,  Appendix,  contains  a  list  of  the  naked-eye  vari- 
ables visible  in  the  United  States. 

Such  variable  stars  as  had  not  names  of  their  own  before  their 
variability  was  discovered  are  at  present  generally  indicated  by  the 
letters  R,  S,  T,  etc.;  i.e.,  R  Sagittarii  is  the  first  discovered  variable  in 
the  constellation  of  Sagittarius,  S  Sagittarii  is  the  second,  etc. 

In  a  considerable  number  of  the  earlier  discovered  variables, 
the  range  of  brightness  is  from  two  to  eight  magnitudes  ; 
that  is,  the  maximum  brightness  exceeds  the  minimum  from 
6  to  1000  times.  In  the  majority,  however,  the  range  is  much 
less,  —  only  a  fraction  of  a  magnitude. 

It  is  worth  noting  that  a  large  proportion  of  the  variables, 
especially  those  of  Classes  IV.  and  V.,  are  reddish  in  their 
color.  This  is  not  true  of  the  Algol  type. 


STAR   SPECTRA. 

<r 

362.  As  early  as  1824  Fraunhofer  observed  the  spectra  of  a 
number  of  bright  stars  by  looking  at  them  with  a  small  tele- 
scope with  a  prism  in  front  of  the  object-glass.  In  1864,  as 
soon  as  the  spectroscope  had  taken  its  place  as  a  recognized 
instrument  of  research,  it  was  applied  to  the  stars  by  Huggins 
and  Secchi.  The  former  studied  very  few  spectra,  but  very 
thoroughly,  with  reference  to  the  identification  of  the  chemi- 
cal elements  in  certain  stars.  He  found  with  certainty  in 
their  spectra  the  lines  of  sodium,  magnesium,  calcium,  iron, 


264          SECCHl's  CLASSES  OF  SPECTRA.         [§  362 

and  hydrogen,  and  more  or  less  doubtfully  a  number  of  other 
metals.  Secchi,  on  the  other  hand,  examined  great  numbers 
of  spectra,  less  in  detail,  but  with  reference  to  a  classification 
of  the  stars  from  the  spectroscopic  point  of  view. 

363.  Secchi's  Classes  of  Spectra.  —  He  made  four  classes, 
as  follows :  — 

I.  Those  which  have  a  spectrum  characterized  by  great  in- 
tensity of  the  dark  lines  of  hydrogen,  all  other  lines  being 
comparatively  feeble  or  absent.     This  class  comprises   more 
than  half  of  all  the  stars,  —  nearly  all  the  white  or  bluish 
stars.     Sirius  and  Vega  are  its  types. 

II.  Those  which  show  a  spectrum  resembling  that  of  the 
sun;    i.e.)   marked  with  a  great  number  of  fine  dark  lines. 
Capella  (Alpha  Aurigse)  and  Pollux  (Beta   Geminorum)   are 
conspicuous  examples.     The  stars  of  this  class  are  also  numer- 
ous.    The   first  and   second  classes   together  comprise   fully 
seven-eighths  of  all  the  stars  whose  spectra  are  known. 

Certain  stars,  like  Procyon  and  Altair,  seem  to  be  intermediate 
between  the  first  and  second  classes.  The  line  of  demarcation  is  by 
no  means  sharp. 

'  III.  Stars  which  show  a  spectrum  characterized  by  dark 
bands,  sharply  defined  at  the  upper  or  more  refrangible  edge, 
aad  shading  out  towards  the  red.  Most  of  the  red  stars,  and 
a  large  number  of  the  variable  stars,  belong  to  this  class. 
Some  of  them  show,  also,  bright  lines  in  their  spectra. 

IV.  This  class  comprises  only  a  few  small  stars,  which,  like 
the  preceding,  show  dark  bands,  but  shading  in  the  opposite 
direction.  Usually  they  also  show  a  few  bright  lines. 

This  classification  is  by  no  means  entirely  satisfactory,  and  various 
modifications  have  been  proposed  for  it  by  Vogel,  Lockyer,  and  others. 
On  the  whole,  however,  we  let  it  stand  as  the  best  known  and  simplest, 
and  sufficient  for  most  purposes. 


§  364]  PHOTOGRAPHY   OF   STELLAR    SPECTRA.  265 

364.  Photography  of  Stellar  Spectra.  —  The  observation  of 
these  spectra  by  the  eye  is  very  tedious  and  difficult,  and  pho- 
tography has  of  late  been  brought  in  most  effectively.  Hug- 
gins,  in  England,  and  Henry  Draper,  in  this  country,  were  the 
pioneers,  but  incomparably  the  finest  results  in  this  line  are 
those  that  have  been  obtained  by  Professor  E.  C.  Pickering,  of 
Cambridge,  in  connection  with  the  Draper  Memorial  Fund. 
Pickering  has  recurred  to  the  old  method  of  Fraunhofer,  using 
a  prism,  or  prisms,  in  front  of  the  object-glass  of  his  photo- 
graphic telescope,  thus  forming  a  "slitless  spectroscope." 
The  edges  of  the  prism,  or  prisms,  are  placed  east  and  west. 
If  the  clock-work  of  the  instrument  followed  the  star  exactly, 
the  spectrum  formed  on  the  sensitive  plate  would  be  a  mere  nar- 
row streak ;  but  by  allowing  the  clock  to  gain  or  lose  slightly, 
the  image  of  the  star  will  move  to  the  east  or  west  by  a 
very  small  quantity  during  the  exposure,  converting  the  streak 
into  a  band.  With  his  large  apparatus,  consisting  of  the 
eleven-inch  telescope  formerly  belonging  to  Dr.  Draper,  and  a 
battery  of  four  enormous  prisms  placed  in  front  of  the  object- 
glass,  spectra  are  obtained  with  an  exposure  of  thirty  minutes, 
which  before  enlargement  are  fully  three  inches  long  from 
the  F  line  to  the  ultra-violet  extremity.  They  easily  bear 


KH  h  Hy  jr 

FIG.  75.  —  Photographic  Spectrum  of  Vega. 

tenfold  enlargement,  and  show  many  hundreds  of  lines  in  the 
spectra  of  the  stars  which  belong  to  Secchi's  second  class. 
Fig.  76  is  from  one  of  these  photographs  of  the  spectrum  of 
Vega.  Of  course  the  photograph  fails  to  show  the  lower  por- 
tion of  the  spectrum,  —  i.e.,  the  red,  yellow,  and  green. 


266  TWINKLING   OF   THE   STARS.  [§  365 

365.  Twinkling  or  Scintillation  of  the  Stars.  —  This  phe- 
nomenon is  purely  physical,  and  not  in  the  least  astronomical.  It 
depends  both  upon  the  irregularities  of  refraction  in  the  air  traversed 
by  the  light  on  its  way  to  the  eye  (due  to  winds  and  differences  of 
temperature),  and  also  on  the  fact  that  the  star  is  optically  a  luminous 
point  without  apparent  size,  —  a  fact  which,  under  the  circumstances, 
gives  rise  to  the  optical  phenomenon  known  as  "interference."  Plan- 
ets which  have  discs  measurable  with  a  micrometer  do  not  sensibly 
twinkle. 

The  scintillation  is  of  course  greatest  near  the  horizon,  and  on  a 
good  night  it  practically  disappears  at  the  zenith.  When  the  image 
of  a  twinkling  star  is  examined  with  the  spectroscope,  dark  inter- 
ference-bands are  seen  moving  back  and  forth  in  its  spectrum. 


3t5<j-l  DOUBLE   STARS.  267 


CHAPTER   XII. 

DOUBLE  AND  MULTIPLE  STARS  AND   CLUSTERS. —  NEBULAE. 
—  DISTRIBUTION    OF    STARS   AND    CONSTITUTION  OF  THE 
STELLAR    UNIVERSE.  —  COSMOGONY    AND    THE    NEBULAR 
HYPOTHESIS. 

366.  Double  Stars. — The  telescope  shows  numerous  cases 
in  which  two  stars  lie  so  near  each  other  that  they  can  be 
separated   only   by   a  high   magnifying   power.       These   are 
"  double  stars,"  and  at  present  more  than  10,000  such  couples 
are  known.      There  is  also  a  considerable  number  of  triple 
stars,  and  a  few  which  are  quadruple.     Fig.  76  represents  a 
few  of  the  best  known  objects  of  each  class.     The  apparent 
distances  generally  range  from  30"  downwards,  very  few  tele- 
scopes being  able  to  separate  stars  closer  than  a  quarter  of  a 
second.     In  a  large  proportion  of  cases  (perhaps  a  third  of  all) 
the  two  components  are  nearly  equal  in  brightness,  but  in 
many  they  are  very  unequal ;  in  that  case  (never  when  they 
are  equal)  they  often  present  contrasts  of  color,  and  when  they 
do,  the  smaller  star  (for  some  reason  not  known)  always  has  a 
tint  higher  in  the  spectrum  than  that  of  the  larger :  if  the  larger 
is  reddish  or  yellow,  the  small  star  will  be   green,  blue,  or 
purple. 

Gamma  Andromedae  and  Beta  Cygni  are  fine  examples  of  colored 
doubles  for  a  small  telescope. 

367.  Stars  Optically  and  Physically  Double.  —  Stars  may 
be  double  in  two  ways,  —  optically  or  physically.     In  the  first 
case  they  are  merely  approximately  in  line  with  each  other,  as 


268  DOUBLE  STARS.  t§  367 

seen  from  the  earth ;  in  the  second  case,  they  are  really  near 
each  other.  In  the  case  of  stars  that  are  only  optically  double, 
it  usually  happens  that  after  some  years  we  can  detect  their 
mutual  independence  in  the  fact  that  their  relative  motion  is  in 


FIG.  76.  —Double  and  Multiple  Stars. 

a  straight  line  and  uniform;  i.e.,  one  of  them  drifts  by  the  other 
in  a  line  which  is  perfectly  straight.  This  is  a  simple  conse- 
quence of  the  combination  of  their  independent  "proper 
motions."  If  they  are  physically  connected,  we  find  on  the 
contrary  that  the  relative  motion  is  in  a  concave  curve;  i.e., 
taking  one  of  them  as  a  centre,  the  other  one  moves  around  it 
in  a  curve. 

The  doctrine  of  chances  shows  what  direct  observation  con- 
firms, that  optical  pairs  must  be  comparatively  rare,  and  that 
the  great  majority  of  double  stars  must  be  really  physically 


§  367]  BINARY   STABS.  269 

connected,    probably   by   the   same   attraction   of   gravitation 
which  controls  the  solar  system. 

368.  Binary  Stars.  —  Stars   thus  physically  connected  are 
also  known  as   "binary"  stars.      They  revolve  in  elliptical 
orbits  around  their  common  centre  of  gravity,  in  periods  which 
range  from  14  years  to  1500  (so  far  as  at  present  known), 
while  the  apparent  length  of  the  ovals  ranges  from  40"  to  0".5. 
The  older  Herschel,  a  little  more  than  a  century  ago,  first  dis- 
covered this  orbital  motion  of  "  binaries  "  in  trying  to  ascertain 
the  parallax  of  some  of  the  few  double  stars  which  were  known 
at  his  time.     It  was  then  supposed  that  they  were  simply  opti- 
cal pairs,  and  he  expected  to  detect  an  annual  displacement  of 
one  member  of  the  pair  with  reference  to  the  other,  from 
which  he  could  infer  its   annual   parallax    (Art.  343).      He 
failed  in  this,  but  found  instead  a  true  orbital  motion.     The 
apparent  orbit  is  always  an  ellipse ;  but  this  apparent  orbit  is 
the  true  orbit  seen  more  or  less  obliquely ;  so  that  the  larger 
star  is  not  usually  in  the  focus  of  the  relative  orbit  pursued  by 
the  smaller  one.     If  we  assume  what  is  probable,  though  cer- 
tainly not  proved  as  yet,  that  the  orbital  motion  of  the  pair  is 
under  the  law  of   gravitation,  we  know  that  the  larger  star 
must  be  in  the  focus  of  the  true  relative  orbit  of  the  smaller, 
and,  moreover,  that  the  latter  must  describe  around  it  equal 
areas  in  equal  times.     By  the  help  of  these  principles  we  can 
deduce  from  the  apparent  oval  the  true  orbital  ellipse;  but 
the  calculation  is  troublesome  and  delicate. 

369.  At  present  the  number  of  pairs  in  which  this  kind  of  motion 
has  been  certainly  detected  is  about  200,  and  it  is  continually  increas- 
ing as  our  study  of  the  double  stars  goes  on.     About  fifty  pairs  have 
progressed  so  far,  either  having  completed  an  entire  revolution  or  a 
large  part  of  one,  that  it  is  possible  to  determine  their  orbits  with 
some  accuracy. 

The  case  of  Sirius  is  peculiar.     Nearly  forty  years  ago  it  had  been 
found  from  meridian-circle  observations  to  be  moving,  for  no  assign- 


270 


SIZE  OF  THE   ORBITS. 


[§  360 


able  reason,  in  a  small  orbit,  with  a  period  of  about  fifty  years.     In 
1862,  Clark,  the  telescope-maker  in  Cambridge,  U.S.,  found  near  it  a 

minute  companion,  which 
explains  everything;  only 
we  have  to  admit  that  this 
faint  attendant,  which  does 
not  give  T2^<r  as  much 
light  as  Sirius  itself,  has  a 
mass  more  than  a  quarter 
part  as  great.  It  seems  to 
be  one  of  Bessel's  dark 
stars.  Fig.  77  represents 

FIG.  77.  -  Orbits  of  Binary  Stare.  the  apparent   Qrbits   of  twQ 

of  the  best  determined  double-star  systems,  Gamma  Virginis  and  Xi 
Ursse  Majoris. 

370.  Size  of  the  Orbits.  — The  real  dimensions  of  a  double- 
star  orbit  can  easily  be  obtained  when  we  know  its  distance 
from  us.  Fortunately,  a  number  of  stars  whose  parallaxes 
have  been  ascertained  are  also  binary ;  and  assuming  the  best 
available  data,  we  have  the  results,  given  in  the  little  table 
which  follows,  the  real  semi-major  axis  of  the  orbit  (in  astro- 

n" 
nomical  units)  being  always  equal  to  the  fraction  — ,  in  which 

a"  is  the  angular  semi-major  axis  of  the  double  star  orbit  in 
seconds  of  arc,  and  p"  the  parallax  of  the  star. 


NAME. 

Assumed 
Parallax. 

Angular 
Serai-axis. 

Real 
Semi-axis. 

Period. 

Mass. 

0=1. 

17  Cassiopeia  
Sirius  

0".15 

0.38 

8".64 
8.58 

57.6 
22.6 

195.y2 
52.0? 

5.0 

4.26? 

a  Geminorum  .... 
a  Centauri  ... 

0.20? 
075 

5.54 
1750 

27.7? 
233 

266 
770 

0.30? 
2  14 

70  Ophiuchi  
61  Cveni 

0.16 
0.43 

4.79 
1540? 

29.9 
358? 

94.5 
4500? 

3.0 
0.23? 

§  ^70]  MASSES   OF  BINARY   STARS.  271 

These  double-star  orbits  are  evidently  comparable  in  magni- 
tude with  the  larger  orbits  of  the  planetary  system,  none  of 
those  given  being  smaller  than  the  orbit  of  Uranus,  and  none 
twice  as  large  as  that  of  Neptune. 

371.  Masses  of  Binary  Stars.  —  If  we  assume  that  the 
binary  stars  move  under  the  law  of  gravitation,  then  when  we 
know  the  semi-major  axis  of  the  orbit  and  the  period  of  revolu- 
tion, we  can  easily  find  the  mass  of  the  pair  as  compared  with 
that  of  the  sun  ;  much  more  easily,  indeed,  than  we  can  deter- 
mine the  mass  of  Mercury  or  the  moon,  strange  as  it  may 
seem.  It  is  done  simply  by  the  following  equation,  which  we 
give  without  demonstration  (see  General  Astronomy,  Arts.  576 
and  838):— 

(If  +m)  =  * 


in  which  (M  +  m)  is  the  united  mass  of  the  two  stars,  S  is  the 
mass  of  the  sun,  a  is  the  semi-major  axis  of  the  orbit  of  the 
double  star  in  astronomical  units,  and  t  its  period  in  years. 
The  final  column  of  the  preceding  table  gives  the  masses  of 
the  star-pairs,  resulting  from  such  data  as  we  now  possess  ; 
but  the  reader  must  bear  in  mind  that  the  margin  of  error  is 
very  considerable,  because  of  the  uncertainty  of  the  orbits  and 
parallaxes  in  question.  A  very  slight  error  in  the  parallax 
makes  a  very  great  error  in  the  resulting  mass. 

372.  Planetary  Systems  attending  Stars.  —  It  is  a  natural  ques- 
tion whether  some  of  the  small  companions  that  we  see  near  large 
stars  may  not  be  the  "  Jupiters  "  of  their  planetary  systems.  We  can 
only  say  as  to  this  that  no  telescope  ever  constructed  could  even  come 
near  to  making  visible  a  planet  which  bears  to  its  primary  any  such 
relations  of  size,  distance,  and  brightness,  as  Jupiter  bears  to  the  sun. 
Viewed  from  our  nearest  neighbor  among  the  stars,  Jupiter  would  be 
a  little  star  of  about  the  21st  magnitude,  not  quite  5"  distance  from 
the  sun,  which  itself  would  look  like  a  star  of  the  second  magnitude. 
To  render  a  star  of  the  21st  magnitude  barely  visible  (apart  from  all 
the  difficulties  raised  by  the  nearness  of  a  larger  star)  would  require 


272  SPECTROSCOPIC   BINARIES.  [§  372 

01 

a  telescope  more  fAan  twenty  feet  in  diameter.  If  any  of  the  stars  have 
planetary  systems  accompanying  them,  we  shall  never  be  likely  to  see 
them  until  our  telescopes  have  attained  a  magnitude  and  power  as  yet 
undreamed  of. 

373.  Spectroscopic  Binaries.  —  One  of  the  most  interesting 
of  recent  astronomical  results  is  the  detection  by  the  spectro- 
scope of  several  pairs  of  double  stars  so  close  that  no  telescope 
can  separate  them.  In  1889  the  bright  component  of  the  well- 
known  double  star  Mizar  (Zeta  Ursse  Majoris,  Fig.  76)  was 
found  by  Pickering  to  show  the  dark  lines  double  in  the  photo- 
graphs of  its  spectrum,  at  regular  intervals  of  about  fifty-two 
days.  The  obvious  explanation  is  that  this  star  is  composed 
of  two,  which  revolve  around  their  common  centre  of  gravity 
in  an  orbit  which  is  turned  nearly  edgewise  towards  us.  (If  it 
was  exactly  edgewise,  the  star  would  be  variable  like  Algol.) 

When  the  stars  are  at  right  angles  to  the  line  from  them  to 
us,  one  of  the  two  will  be  moving  towards  us,  while  the.  other 
is  moving  in  an  opposite  direction  ;  and  as  a  consequence, 
the  lines  in  their  spectra  will  be  shifted  opposite  ways,  accord- 
ing to  Doppler's  principle  (Art.  179).  Now  since  the  two 
stars  are  so  close  that  their  spectra  overlie  each  other,  the 
result  will  be  simply  to  make  the  lines  in  the  compound  spec- 
trum look  double.  From  the  distance  apart  of  the  lines,  the 
relative  velocity  of  the  stars  can  be  found,  and  from  this  the 
size  of  the  orbit  and  the  mass  of  the  stars.  Thus  it  appears 
that  in  the  case  of  Mizar  the  relative  velocity  of  the  two 
components  is  about  100  miles  per  second,  the  period  about 
104  days,  and  the  distance  between  the  two  stars  about  the 
same  as  the  diameter  of  the  orbit  of  Mars ;  from  which  it  fol- 
lows that  their  united  mass  is  about  forty  times  that  of  the 
sun. 

This  makes  Mizar  really  a  triple  star,  the  larger  of  the  two  that  are 
seen  with  a  small  telescope  being  the  one  that  is  thus  spectroscopically 
split. 


§  374]  SPECTROSCOPIC   BINARIES.  273 

374.  The  lines  in  the  spectrum  of  Beta  Aurigae  exhibit  the 
same  peculiarity,  but  the  doubling  occurs  once  in  four  days ; 
the  velocity  being  about  150  miles  a  second,  and  the  diameter 
of  the  orbit  about  8,000000  miles,  while  the  united  mass  of  the 
two  stars  is  about  two  and  a  half  times  that  of  the  sun. 

These  observations  of  Professor  Pickering's  were  made  by 
photographing  the  spectrum  with  the  slitless  spectroscope  (Art. 
364),  and  are  possible  only  where  the  stars  which  compose  the 
binary  are  both  of  them  reasonably  bright. 

With  his  slit-spectroscope,  Vogel  (Art.  341),  as  has  already 
been  stated  (Art.  360),  has  been  able  to  detect  a  similar  orbital 
motion  in  Algol,  although  the  companion  of  the  brighter  star 
is  itself  invisible.  More  recently,  in  the  case  of  the  bright 
star  Alpha  Virginis  (Spica),  he  has  found  a  result  of  the  same 
kind.  At  first  the  photographic  observations  of  the  spectrum 
of  this  star  appeared  very  discordant.  Some  days  they  indi- 
cated that  the  star  was  moving  toivards  us  quite  rapidly,  and 
then  again  from  us  ;  but  it  is  found  that  everything  can  be 
explained  by  the  simple  supposition  that  the  star  is  double 
with  a  small  companion,  like  that  of  Algol,  not  bright  enough 
to  show  itself  by  its  light,  but  heavy  enough  to  make  its  part- 
ner swing  around  in  an  orbit  about  6,000000  miles  in  diameter, 
once  in  four  days,  —  the  orbit  not  being  quite  edgewise  to  the 
earth,  so  that  the  dark  companion  does  not  eclipse  Spica,  as 
Algol  is  eclipsed  by  its  attendant.  Bigel  (Beta  Orionis)  also 
shows  traces  of  a  similar  periodic  variation,  though  the  obser- 
vations have  not  yet  been  continued  long  enough  to  deter- 
mine its  period  precisely.  It  is  likely  that  a  large  number  of 
similar  double  stars  will  thus  be  found  by  the  spectroscope 
before  very  long.  These  orbits,  of  course,  are  very  much 
smaller  than  those  of  most  of  the  telescopic  binaries. 

375.  Multiple    Stars    (see  Fig.   76).  —  In    a    considerable 
number  of  cases  we  find  three  or  more  stars  connected  in  one 
system.     Zeta  Cancri  consists  of  a  close  pair  revolving  in  a 


274  MULTIPLE   STARS — CLUSTERS.  [§  3?5 

nearly  circular  orbit,  with  a  period  somewhat  less  than  sixty 
years,  while  a  third  star  revolves  in  the  same  direction  around 
them,  at  a  much  greater  distance,  and  with  a  period  not  less 
than  500  years  (not  yet  fully  determined).  Moreover,  this 
third  star  is  subject  to  a  peculiar  irregularity  in  its  motion, 
which  seems  to  indicate  that  it  has  an  invisible  companion 
very  near  the  system,  the  system  being  really  quadruple. 

In  Epsilon  Lyrse  we  have  a  most  beautiful  quadruple  sys- 
tem, composed  of  two  pairs,  each  binary  with  a  period  of  over 
200  years.  Moreover,  since  they  have  a  common  proper 
motion,  it  is  probable  that  the  two  pairs  revolve  around 
each  other  in  a  period  which  can  be  reckoned  only  in  thou- 
sands of  years.  In  Theta  Orionis,  we  have  a  remarkable  object, 
in  which  the  six  components  are  not  organized  in  pairs,  but 
are  at  not  very  unequal  distances  from  each  other. 

376.  Clusters.  —  There  are  in  the  sky  numerous  groups  of 
stars,  containing  from  a  hundred  to  many  thousand  members. 
A  few  of  them  are  resolvable  by  the  naked  eye,  as,  for  in- 
stance, the  Pleiades  (Fig.  78) ;  some,  like  Praesepe  in  Cancer, 
break  up  under  the  power  of  even  an  opera-glass  (Art.  52); 
but  most  of  them  require  a  large  telescope  to  show  the  sepa- 
rate components.  To  the  naked  eye  or  small  telescopes,  if 
visible  at  all,  they  look  like  faint  clouds  of  shining  haze  ;  but 
in  a  great  telescope  they  are  among  the  most  magnificent 
objects  the  heavens  afford.  The  cluster  known  as  "13  Mes- 
sier," not  far  from  the  "  apex  of  the  sun's  way,"  is  perhaps 
the  finest. 

The  question  at  once  arises  whether  the  stars  in  such  a 
cluster  are  comparable  with  our  own  sun  in  magnitude,  and 
separated  from  each  other  by  distances  like  that  between  the 
sun  and  Alpha  Centauri,  or  whether  they  are  really  small  (for 
stars)  and  closely  packed,  —  whether  the  swarm  is  about  the 
same  distance .  from  us  as  the  rest  of  the  stars,  or  far  beyond 
them. 


§  376]  THE  PLEIADES.  275 

Forty  years  ago  the  prevalent  view  was  that  these  clusters 
were  stellar  universes,  galaxies,  like  the  group  of  stars  to 
which  it  was  supposed  the  sun  belongs,  — but  so  inconceivably 
remote  that  they  dwindled  to  mere  shreds  of  cloud.  It  is  now, 


Astcrope 

+K 

\    : , ,     Q  Taygeta 

"" 


^c.  Pleione        ..-•''       A  *•     /I  M  V . 

•'"      -  Jf>-  •  .;.:.-•"/  '•-'.•.•::: ^T?^-- 

Alcyone;S"  Electro, 

M.  * :•.••'  .,;    :^.:^\r::.v::.vf-'--- 

,;:>'' /v/Merope 


FIG.  78.  — The  Pleiades. 

however,  quite  certain  that  the  opposite  view  is  correct.  The 
star  clusters  are  among  our  stars,  and  form  a  part  of  our  own 
stellar  universe.  Large  and  small  stars  are  so  associated  in 
the  same  group  as  to  leave  no  doubt  on  this  point,  although 
it  has  not  yet  been  possible  to  determine  the  actual  parallax 
and  distance  of  any  cluster. 


276 


GREAT  NEBULA  IN  ANDROMEDA. 


[§377 


NEBULAE. 

377.  Besides  the  luminous  clouds  which,  under  the  tele- 
scope, break  up  into  separate  stars,  there  are  others  which  no 
telescopic  power  resolves,  and  among  them  some  which  are 
brighter  than  many  of  the  clusters.  These  irresolvable  <5b- 

jects,  which  now  number 
more  than  8000,  are  "neb- 
ulae." Two  or  three  of 
them  are  visible  to  the 
naked  eye ;  one,  the  bright- 
est of  all,  and  the  one  in 
which  the  temporary  star 
of  1885  appeared,  is  in  the 
constellation  of  Androm- 
eda (see  Fig.  79).  An- 
other most  conspicuous 
and  very  beautiful  nebula 
is  that  in  the  sword  of 
Orion. 

The  larger  and  brighter 
nebulae  are,  for  the  most 
part,  irregular  in  form, 
sending  out  sprays  and 
streams  in  all  directions, 
and  containing  dark  openings  and  "lanes."  Some  of  them 
are  of  enormous  volume.  The  great  nebula  of  Orion  (which 
includes  within  its  boundary  the  multiple  star,  Theta  Orionis) 
covers  several  square  degrees.1 

The  nebula  of  Andromeda  is  not  quite  so  extensive,  but  is 
rather  more  regular  in  its  form. 

1Very  recently  photographs  taken  at  Wilson's  Peak,  Cal.,  show  that 
nearly  the  whole  constellation  is  enveloped  in  nebulosity,  the  wisps  attach- 
ing themselves  especially  to  most  of  the  principal  stars. 


FIG.  79.  —  Telescopic  View  of  the  Great  Nebula 
in  Andromeda. 


§377] 


ANNULAR   NEBULA  IN   LYRA. 


277 


The  smaller  nebulae  are,  for  the  most  part,  more  or  less 
nearly  oval,  and  brighter  in  the  centre.  In  tfie  so-called 
"  nebulous  stars,'7  the  cen- 
tral nucleus  is  like  a  star 
shining  through  a  fog. 
The  "planetary  nebulae" 
are  about  circular  and 
have  nearly  a  uniform 
brightness  throughout, 
while  the  rare  "  annular  " 
or  "ring  nebulae"  are 
darker  in  the  centre.  Fig. 
80  is  a  representation  of 
the  finest  of  these  annular 
nebulae,  that  in  the  con- 
stellation of  Lyra.  There 
are  a  number  of  nebulae 
which  exhibit  a  remark- 
able spiral  structure  in 
large  telescopes.  There 
are  several  double  nebulae, 
and  a  few  that  are  variable  in  brightness,  though  no  regular- 
ity has  yet  been  ascertained  in  their  variation. 

The  great  majority  of  the  8000  nebulae  are  extremely  faint, 
even  in  large  telescopes,  but  the  few  that  are  reasonably  bright 
are  very  interesting  objects. 

378,  Drawings  and  Photographs  of  Nebulae,  —  Until  very 
lately  the  correct  representation  of  a  nebula  was  an  extremely 
difficult  task.  More  or  less  elaborate  engravings  exist  of  per- 
haps fifty  of  the  more  conspicuous  of  them,  but  photography 
has  now  taken  possession  of  the  field.  The  first  success  in 
this  line  was  by  Henry  Draper  of  New  York,  in  1880,  in  pho- 
tographing the  nebula  of  Orion.  Since  his  death,  in  1882, 
great  progress  has  been  made  both  in  Europe  and  in  this 


FIG.  80.  —  The  Annular  Nebula  in  Lyra. 


278 


PHOTOGRAPHS   OF   NEBULA. 


[§378 


country,   and   at   present    the    photographs    are    continually 
bringing  out  new  and  before  unsuspected  features.     Fig.  81, 


FIG.  81.  — Mr.  Roberts's  Photograph  of  the  Nebula  of  Andromeda. 

for  instance,  is  from  a  photograph  of  the  nebula  of  Androm- 
eda, taken  by  Mr.  Roberts  of  Liverpool  in  1888,  and  shows 


§  378]  PHOTOGRAPHS   OF   NEBULA.  279 

that  the  so-called  "  dark  lanes,"  which  hitherto  had  been  seen 
only  as  straight  and  wholly  mysterious  markings  (Fig.  79), 
are  really  curved  ovals,  like  the  divisions  in  Saturn's  rings. 
The  photograph  brings  out  clearly  a  distinct  annular  structure 
pervading  the  whole  nebula,  which  as  yet  has  never  been 
made  out  satisfactorily  by  the  eye  with  any  telescope. 

The  photographs  not  only  show  new  features  in  old  nebulae,  but 
they  reveal  numbers  of  new  nebulae  invisible  to  the  eye  with  any  tele- 
scope. Thus,  in  the  Pleiades  it  has  been  found  that  almost  all  the 
larger  stars  have  wisps  of  nebulosity  attached  to  them,  as  indicated  by 
the  dotted  lines  in  Fig.  78 ;  and  in  a  small  territory,  in  and  near  the 
constellation  of  Orion,  Pickering,  with  an  eight-inch  telescope,  found 
upon  his  star-plates  nearly  as  large  a  number  of  new  nebulae  as  of 
those  that  were  previously  known  within  the  same  boundary. 

The  photographs  of  nebulse  require  generally  an  exposure  of  from 
one  to  two  hours.  The  images  of  all  the  brighter  stars  that  fall  upon 
the  plate,  are,  therefore,  always  immensely  over-exposed,  and  seriously 
injure  the  picture  from  an  artistic  point  of  view. 

The  photographic  brightness  of  a  nebula,  to  use  such  an  expression, 
is  many  times  greater  than  its  brightness  to  the  eye,  owing  to  the  fact 
that  its  light  consists  mainly  in  rays  which  belong  to  the  upper  or 
blue  portion  of  the  spectrum.  It  has  very  little  red  or  yellow  in  it. 
At  least,  this  is  so  with  all  the  nebulae  whose  spectra  are  characterized 
by  bright  lines. 

379.  Changes  in   Nebulae.  —  It  cannot  be  stated  with  certainty 
that  sensible  changes  have  occurred  in  any  of  the  nebulse  since  they 
first  began  to  be  observed,  —  the  early  instruments  were  so  inferior  to 
modern  ones  that  the  older  drawings  cannot  be  trusted ;  but  some  of 
the  differences  between  the  older  and  more  recent  representations  make 
it  extremely  likely  that  real  changes  are  going  on.     Probably  after  a 
reasonable  interval  of  time  photography  will  settle  the  question. 

380.  Spectra  of  Nebulae.  —  One  of  the  most  important  of 
the  early  achievements  of  the  spectroscope  was  the  proof  that 
the   light  of   many  nebulae,  if  not  all,  proceeds  from  glow- 
ing gas  of  low  density,  and  not  from  aggregations  of  stars. 


280  SPECTRA   OF  NEBULAE.  [§  380 

Huggins,  in  1864,  first  made  the  decisive  observation  by  find- 
ing bright  lines  in  their  spectra.  Thus  far  the  spectra  of  all  the 
nebulae  that  show  lines  at  all  appear  to  be  substantially  the 
same.  Four  lines  are  usually  easily  observed,  two  of  which 
are  due  to  hydrogen ;  but  the  other  two,  which  are  brighter 
than  the  hydrogen  lines,  are  not  yet  identified. 

At  one  time  the  brightest  of  the  four  lines  was  thought  to  be  due 
to  nitrogen,  and  even  yet  the  statement  that  such  is  the  case  is  found 
in  many  books  ;  but  it  is  now  certain  that,  whatever  it  may  be,  nitro- 
gen is  not  the  substance.  Very  recently  Mr.  Lockyer  has  ascribed  this 
line  to  magnesium,  in  connection  with  his  meteoric  hypothesis.  But 
recent  elaborate  observations  of  Huggins  and  others  show  that  this 
identification  also  is  probably  incorrect. 

Fig.  82  shows  the  position  of  the  principal  lines  so  far  as  observed. 
In  the  brighter  nebulae  a  number  of  others  are  also  sometimes  seen. 
Mr.  Huggins's  recent  photographic  spectrum  of  the  nebula  of  Orion 


FIG.  82.  —  Spectrum  of  the  Gaseous  Nebulas. 

shows,  in  addition  to  those  that  are  visible  to  the  eye,  a  number  of 
bright  lines  in  the  ultra-violet;  and,  what  is  interesting,  these  lines 
seem  to  pertain  also  to  the  spectrum  of  the  stars  in  the  so-called 
"  Trapezium "  (Theta  Orionis),  as  if  (which  is  very  likely)  the  stars 
themselves  were  mere  condensations  of  nebulous  matter. 

381.  Not  all  nebulae  show  the  bright-line  spectrum.  Those 
which  do  (about  half  the  whole  number)  are  of  a  greenish  tint, 
at  once  recognizable  in  a  large  telescope.  The  white  nebulae, 
with  the  nebula  of  Andromeda,  the  brightest  of  all,  at  their 
head,  present  only  a  plain  continuous  spectrum,  unmarked  by 


§  381]       DISTANCE  AND  DISTRIBUTION   OF   NEBULAE.         281 

lines  of  any  kind.  This,  however,  does  not  necessarily  indicate 
that  the  luminous  matter  is  not  gaseous,  for  a  gas  under  pres- 
sure gives  a  continous  spectrum,  like  an  incandescent  solid  or 
liquid.  The  telescopic  evidence  as  to  the  non-stellar  consti- 
tution of  nebulae  is  the  same  for  all;  no  nebula  resists  all 
attempts  at  resolution  (i.e.,  breaking  up  into  stars)  mojre  stub- 
bornly than  that  of  Andromeda.1 

As  to  the  real  constitution  of  those  bodies,  we  can  only 
speculate.  The  fact  that  the  luminous  matter  in  them  is 
mainly  gaseous  does  not  at  all  make  it  certain  that  they  do 
not  also  contain  dark  matter,  either  liquid  or  solid.  What 
proportion  of  it  there  may  be,  we  have  at  present  no  means 
of  knowing. 

382.  Distance  and  Distribution  of  Nebulae. — As  to  the  dis- 
tance, we  can  only  say  that,  like  the  star  clusters,  they  are 
within  the  stellar  universe  and  not  beyond  its  boundaries. 
This  is  clearly  shown  by  the  nebulous  stars,  first  pointed  out 
and  discussed  by  the  older  Herschel.  We  find  all  gradations, 
from  a  star  with  a  little  faint  nebulosity  around  it,  to  nebulae 
which  show  only  the  faintest  spot  of  light  in  the  centre.  It  is 
confirmed  also  by  such  peculiar  associations  of  the  stars  and 
nebulae  as  we  find  in  the  Pleiades.  Moreover,  in  certain  curi- 
ous luminous  masses,  known  as  the  "Nubeculae,"  near  the 
south  pole,  we  have  stars,  star  clusters,  and  nebulae  promis- 
cuously intermingling. 

Taking  the  sky  generally,  however,  the  distribution  of  the 
nebulae  is  in  contrast  with  that  of  the  stars.  The  stars,  as  we 
shall  see,  crowd  together  near  the  Milky  Way.  The  nebulae, 
on  the  other  hand,  are  most  numerous  just  where  the  stars  are 
fewest,  as  if  the  stars  had  somehow  used  up  the  substance  of 
which  the  nebulae  are  made. 

1  Some  years  ago  it  was  stated  that  Lord  Rosse's  telescope  had  partially 
resolved  the  nebula  of  Andromeda  and  the  nebula  of  Orion.  This  turned 
out  to  be  a  mistake. 


282  THE  MILKY   WAY.  [§  383 


THE   SIDEREAL   HEAVENS. 

383.  The  Galaxy,  or  Milky  Way.  —  This  is  a  luminous  belt 
of  irregular  width  and  outline,  which  surrounds  the  heavens 
nearly  in  a  great  circle.     It  is  very  different  in  brightness  in 
different  parts,  and  is  marked  here  and  there  by  dark  bars  and 
patches,  which  at  night  look  like  overlying  clouds.     For  about 
a  third  of  its   length   (between   Cygnus   and   Scorpio)  it  is 
divided  into   two   roughly  parallel  streams.      The   telescope 
shows  it  to  be  made  up  almost  entirely  of  small  stars  from 
the  eighth  magnitude  down ;  it  contains,  also,  numerous  star 
clusters,  but  very  few  true  nebulae. 

The  galaxy  intersects  the  ecliptic  at  two  opposite  points  not 
far  from  the  solstices,  and  at  an  angle  of  nearly  60°,  the  north 
"  galactic  pole  "  being,  according  to  Herschel,  in  the  constella- 
tion of  Coma  Berenices.  As  Herschel  remarks,  — 

"The  'galactic  plane'  is  to  the  sidereal  universe  much  what  the 
plane  of  the  ecliptic  is  to  the  solar  system,  —  a  plane  of  ultimate  refer- 
ence, and  the  ground  plan  of  the  stellar  system." 

384.  Distribution  of  Stars  in  the  Heavens. —  It  is  obvious 
that  the  distribution  of  the  stars  is  not  even  approximately 
uniform.     They  gather  everywhere  into  groups  and  streams ; 
but,  besides  this,  the  examination  of  any  of  the  great  star- 
catalogues  shows  that  the  average  number  to  a  square  degree 
increases  rapidly  and  pretty  regularly  from  the  galactic  pole  to 
the  galaxy  itself,  where  they  are  most  thickly  packed.     This 
is  best  shown  by  the  "star-gauges  "  of  the  older  Herschel,  each 
of  which  consists  merely  in  an  enumeration  of  the  stars  visi- 
ble in  a  single  field  of  view.     He  made  3400  of  these  gauges, 
and  his  son  followed  up  the  work  at  the  Cape  of  Good  Hope 
with   2300   more   in   the   south   circumpolar    regions.     From 
these  data  it  appears  that  near  the  pole  of  the  galaxy,  the 
average  number  of   stars  in  a  single  field  of  view  is  only 


§  384]        STRUCTURE  OF  THE  STELLAR  UNIVERSE.  283 

about  4 ;  at  45°  from  the  galaxy,  a  little  over  10 ;  while  on  the 
galactic  circle  itself  it  is  122. 

Herschel,  starting  from  the  unsound  assumption  that  the  stars  are 
all  of  about  the  same  size  and  brightness  and  separated  by  approxi- 
mately equal  distances,  drew  from  his  observations  numerous  untenable 
conclusions  as  to  the  form  and  structure  of  the  "  galactic  cluster  "  to 
which  the  sun  was  supposed  to  belong,  —  theories  for  a  time  widely 
accepted,  and  even  yet  more  or  less  current  in  popular  text-books, 
though  in  many  points  certainly  incorrect. 

But  although  the  apparent  brightness  of  the  stars  does  not 
depend  entirely,  or  even  mainly,  upon  their  distance,  it  is  cer- 
tain that  as  a  class  the  faint  stars  are  really  more  remote,  as 
well  as  smaller  and  darker  than  the  brighter  ones.  We  may, 
therefore,  safely  draw  a  few  inferences,  which,  so  far  as  they 
go,  in  the  main  agree  with  those  of  Herschel. 

385.  Structure  of  the  Stellar  Universe.  —  I.  The  great  ma- 
jority of  the  stars  we  see  are  included  within  a  space  having, 
roughly,  the  form  of  a  rather  thin,  flat  disc,  like  a  watch,  with 
a  diameter  eight  or  ten  times  as  great  as  its  thickness,  our 
sun  being  not  very  far  from  its  centre. 

II.  Within  this  space  the  naked-eye  stars  are  distributed 
with  some  uniformity,  but  not  without  a  tendency  to  cluster, 
as  shown  in  the  Pleiades.     The  smaller  stars,  on  the  other 
hand,  are  strongly  "  gregarious,"  and  are  largely  gathered  into 
groups  and  streams  which  have  comparatively  vacant  spaces 
between  them. 

III.  At  right  angles  to  the  galactic   plane  the  stars  are 
scattered  more  evenly  and  thinly  than  in  it,  and  we  find  on 
the  sides  of  the  disc  the  comparatively  starless  region  of  the 
nebulae. 

IV.  As  to  the  Milky  Way  itself,  it  is  not  certain  whether 
the  stars  which  compose  it  form  a  sort  of  thin,  flat,  continu- 
ous sheet,  or  whether  they  are  arranged  in  a  sort  of  ring  with 


284  DO  THE  STAES  FORM  A  SYSTEM  ?  [§  385 

a  comparatively  empty  space  in  the  middle,  where  the  sun  is 
situated,  not  far  from  its  centre. 

As  to  the  size  of  the  disc-like  space  which  contains  most  of  the 
stars,  very  little  can  be  said  positively.  Its  diameter  must  be  as  great 
as  20,000  or  30,000  light-years,  —  how  much  greater  it  may  be  we  can- 
not even  guess;  and  as  to  the  "beyond,"  we  are  still  more  ignorant. 
If,  however,  there  are  other  stellar  systems  of  the  same  order  as  our 
own,  these  systems  are  neither  the  nebulae,  nor  the  clusters  which  the 
telescope  reveals,  but  are  far  beyond  the  reach  of  any  instrument  at 
present  existing. 

386.  Do  the  Stars  form  a  System  ?  —  It  is  probable  (though 
not  certain)  that  gravitation  operates   between  the  stars,  as 
indicated  by  the  motion  of  the  binaries.     The  stars  are  cer- 
tainly moving   very  swiftly  in  various   directions,   and  the 
question  is  whether   these  motions  are  governed  by  gravita- 
tion, and  are  "  orbital "  in  the  ordinary  sense  of  the  word. 

There  has  been  a  very  persistent  belief  that  somewhere 
there  is  an  enormous  central  sun,  around  which  the  stars  are 
all  circulating  in  the  same  way  as  the  planets  of  the  solar 
system  move  about  our  own  sun.  This  belief  has  been  abun- 
dantly proved  to  be  unfounded.  It  is  now  certain  that  there 
is  no  such  great  body  dominating  the  stellar  universe. 

387.  Maedler's  Hypothesis.  —  Another  less  improbable  doc- 
trine is  that  there  is  a  general  revolution  of  the  mass  of  stars 
around  the  centre  of  gravity  of  the  whole, — a  revolution  nearly 
in  the  plane  of  the  Milky  Way.    Some  years  ago,  Maedler,  in 
his  speculations,  concluded  (though  without  sufficient  reason) 
that  this  centre  of  gravity  of  the  stellar  system  was  not  far 
from  Alcyone,  the  brightest  of  the  Pleiades,  and,  therefore, 
that  this  star  was  in  a  sense  the  'central  sun';  and  the  idea 
is  frequently  met  with  in  popular  writings.    It  has  no  basis  of 
reason,  however,  nor  is  there  yet  proof  or  probability  of  any 
such  general  revolution. 


§  388]  COSMOGONY.  285 

388.  On  the  whole,  the  most  reasonable  view  seems  to  be 
that  the  stars  are  moving  much  as  bees  do  in  a  swarm,  each 
star  mainly  under  the  control  of  the  attraction  of  its  nearest 
neighbors,  though  influenced  more  or  less,  of  course,  by  that 
of  the  general  mass.     If  so,  the  paths  of  the  stars  are  not 
"  orbits  "  in  the  strict  sense ;  that  is,  they  are  not  paths  which 
return  into  themselves,  the  forces  which  at  any  moment  act 
upon  a  given  star  being  so  nearly  balanced  that  its   motion 
must  be  sensibly  in  a  straight  line  for  thousands  of  years  at 
a  time. 

The  solar  system  is  an  absolute  despotism,  the  sun  supreme. 
Among  the  stars,  on  the  other  hand,  there  is  no  central  power, 
but  the  system  is  a  pure  democracy,  in  which  the  individuals 
are  controlled  by  the  influence  of  their  neighbors,  and  by  the 
authority  of  the  whole  community  to  which  they  themselves 
belong. 

COSMOGONY. 

389.  One  of  the  most  interesting  topics  of  speculation  re- 
lates to  the  process  by  which  the  present  state  of  things  has 
come  about.     In  a  forest,  to  use  an  old  comparison  of  Her- 
schel's,  we  see  around  us  trees  in  all  stages  of  their  life-his- 
tory, from  the  sprouting  seedlings  to  the  prostrate  and  decaying 
trunks  of  the  dead.     Is  the  analogy  applicable  to  the  heavens, 
and  can  we  hope  by  a  study  of  the  present   condition  and 
behavior  of  the  bodies  around  us  to  come  to  an  understanding 
of  their  past  history  and  probable  future  ?     Possibly  to  some 
extent.      But  human  life  is  so  short  that   the   processes  of 
change  are  hardly  perceptible,  and  our  telescopes  and  spectro- 
scopes reveal  but  little  of  the  "  true  inwardness  "  of  things,  so 
that  speculation  is   continually  baffled,  and  its   results  can 
seldom  be  accepted  as  secure.     Still,  some  general  conclusions 
seem  to  have  been  reached,  which  are  likely  to  be  true ;   but 
the  pupil  is  warned  that  they  are  not  to  be  regarded  as  estab- 


GENESIS   OF   THE   PLA>TETARY   SYSTEM. 

listed  in  any  such  sense  as  the  law  of  gravitation  and  the 
theory  of  planetary  motion. 

In  a  general  way  we  may  say  that  the  shrinkage  of  clouds 
of  rarefied  matter  into  more  compact  masses  under  the  force  of 
gravitation,  the  production  of  heat  by  this  shrinkage,  the  effect 
of  this  heat  upon  the  mass  itself  and  upon  neighboring  bodies, 
—  these  principles  cover  nearly  all  the  explanations  that  can 
thus  far  be  given  for  the  present  condition  of  the  heavenly 
bodies. 

390.  Genesis  of  the  Planetary  System.  —  Ourplanetar; 
tern  is  clearly  no  accidental  aggregation  of  bodies.  Masses  of 
matter  coining  haphazard  to  the  sun  would  move  (as  comets 
actually  do  move)  in  orbits  which,  though  necessarily  conic 
sections,  would  have  every  degree  of  inclination  and  eccen- 
tricity. In  the  planetary  system  this  is  not  so.  Numerous 
relations  exist  for  which  gravitation  does  not  at  all  account, 
and  for  which  the  mind  demands  an  explanation. 

We  note  the  following  as  the  principal :  — 

1.  The  orbits  of  the  planets  are  all  nearly  circular  (i.e-,  never  very 
eccentric). 

2.  They  are  all  nearly  in  one  plane  (excepting  those  of  some  of  the 
asteroids). 

3.  The  revolution  of  all,  without  exception,  is  in  the  same  direction. 

4.  There  is  a  curious  and  regular  progression  of  distances  (ex- 
pressed by  Bode's  Law;  which,  however,  breaks  down  with  Xeptone). 

As  regards  the  planets  themselves  :  — 

5.  The  plane  of  erery  planet's  rotation  nearly  coincides  with  that 
of  its  orbit  (probably  excepting  Uranus). 

6.  The  direction  of  rotation  is  the  same  as  that  of  the  orbital  revo- 
lution (excepting,  probably,  Uranus  and  Neptune). 

7.  The  plane  of  orbital  revolution  of  the  planet's  satellites  coincides 
nearly  with  that  of  the  planet's  rotation,  wherever  this  has  been  ascer- 
tained. 

8.  The  direction  of  the  satellites'  revolution  also  coincides  with  that 
of  the  planet's  revolution  (with  the  same  limitation). 

9.  The  largest  planets  rotate  most  swiftly. 


§  391]  LAPLACE'S  NEBULAE  HYPOTHESIS. 

391.  Sow  this  arrangement  is  certainly  an  admirable  one 
for  a  planetary  system,  and  therefore  some  hare  argued  that 
the  Deity  constructed  the  system  in  that  way,  perfect  from 
the  first.     But  to  one  who  considers  the  way  in  which  other 
perfect  works  usually  attain  their  perfection,  —  their  processes 
of  growth  and  development,  —  this  explanation  seems  improba- 
ble.    It  appears  far  more  likely  that  the  planetary  system  was 
formed  by  growth  than  that  it  was  built  outright.     The  theory 
which,  in  its  main  features,  is  now  generally  accepted,  as  sup- 
plyiiig  an  intelligible  explanation  of  the  facts,  is  that  known 
as  the  "nebular  hypothesis."      In  a  more  or  less  crude  and 
unscientific  form,  it  was  first  suggested  by  Swedenborg  and 
Kant,  and  afterwards,  about  the  beginning  of  the  present  cen- 
tury, was  worked  out  in  mechanical  detail  by  Laplace.    On  the 
whole,  we  may  say  that  while,  in  its  main  outlines,  the  theory 
is  probably  true,  it  also  probably  needs  serious  modifications  in 
its  details. 

392.  Laplace's  Nebular  Hypothesis. — He   maintained   (a) 
that   at  some   time  in  the  past1  the   matter  which  is   now 
gathered  into  the   sun   and  planets  was   in  the  form  of  a 
"nebula." 

(6)  This  nebula,  according  to  him,  was  a  cloud  of  intensely 
heated  gas  (questionable). 

•  (c)  Under  the  action  of  its  own  gravitation,  the  nebula 
assumed  a  form  approximately  globular,  with  a  motion  of  rota- 
tion, the  whirling  motion  depending  upon  the  accidental  differ- 
ences in  the  original  velocities  and  densities  of  the  different 

1  As  to  the  origin  of  the  nebula  itself,  he  did  not  speculate.  There  was 
no  assumption  on  his  part,  as  is  often  supposed,  that  the  matter  was  first 
created  in  the  nebulous  condition.  He  assumed  only  that  as  the  egg  may 
be  taken  as  the  starting-point  in  the  life-history  of  an  animal,  so  the 
nebula  is  to  be  regarded  as  the  starting-point  of  the  life  history  of  the 
planetary  system.  He  did  not  raise  the  question  whether  the  egg  is  older 
than  the  hen  or  not. 


288  LAPLACE'S  NEBULAR  HYPOTHESIS.  [§  392 

parts  of  the  nebula.  As  the  contraction  proceeded,  the  swift- 
ness of  the  rotation  would  necessarily  increase  for  mechanical 
reasons. 

(d)  In  consequence  of  its  whirling  motion,  the  globe  would 
necessarily  become  flattened  at  the  poles,  and  ultimately,  as 
the  contraction  went  on,  the  centrifugal  force  at  the  equator 
would  there  become  equal  to  gravity,  and  rings  of  nebulous 
matter  would  be  detached  from  the  central  mass,  like  the  rings 
of  Saturn.     In  fact,  Saturn's  rings  suggested  this  feature  of 
the  theory. 

(e)  The  ring  thus  formed  would  for  a  time  revolve  as  a 
whole,  but  would  ultimately  break,  and  the  material  would  col- 
lect into  a  globe  revolving  around  the  central  nebula  as  a  planet.1 

Laplace  supposed  that  the  ring  would  revolve  as  if  it  were 
solid,  the  particles  at  the  outer  edge  moving  more  swiftly  than 
those  at  the  inner  (questionable).  If  this  were  always  so,  the 
planet  formed  would  necessarily  rotate  in  the  same  direction 
in  which  the  ring  had  revolved. 

(/)  The  planet  thus  formed  would  throw  off  rings  of  its 
own,  and  so  form  for  itself  a  system  of  satellites. 

393.  This  theory  obviously  explains  most  of  the  facts  of  the 
solar  system,  which  were  enumerated  in  the  preceding  article, 
though  some  of  the  exceptional  facts  (such  as  the  short 
periods  of  the  satellites  of  Mars,  and  the  retrograde  motions  of 
those  of  Uranus  and  Neptune)  cannot  be  explained  by  it  alone 
in  its  original  form.  But  even  these  exceptions  do  not  contra- 
dict it,  as  is  sometimes  supposed. 

As  to  the  modifications  required  by  the  theory,  while  they 
alter  the  mechanism  of  the  development  in  some  respects,  they 
do  not  touch  the  main  results.  It  is  rather  more  likely,  for 
instance,  that  the  original  nebula  was  a  cloud  of  ice-cold  dust 

1  It  has  been  suggested  by  Huggins  and  others  that  the  two  small  neb- 
ulae near  the  great  nebula  of  Andromeda  (Fig.  81)  may  be  planets  in 
process  of  formation. 


§  393]  LOCKYER'S  METEORIC  HYPOTHESIS.  289 

than  incandescent  gas  and  "fire-mist/'  to  use  a  favorite  expres- 
sion; and  it  is  likely  that  planets  and  satellites  were  often 
separated  from  the  mother-orb  otherwise  than  in  the  form  of 
rings. 

Nor  is  it  possible  that  a  thin,  wide  ring  could  revolve  in 
the  same  way  as  a  solid  mass;  the  particles  near  the  inner 
edge  must  make  their  revolution  in  periods  much  shorter  than 
those  upon  the  circumference,  or  the  ring  would  tear  to  pieces. 
But  this  very  fact  makes  it  possible  to  account  for  the  peculiar 
backward  motion  of  the  satellites  of  Uranus  and  Neptune, 
thus  removing  one  of  the  main  objections  to  the  theory  in  its 
original  form. 

Many  things,  also,  make  it  questionable  whether  the  outer 
planets  are  so  much  older  than  the  inner  ones,  as  Laplace's 
theory  would  indicate.  It  is  not  impossible  that  they  may 
even  be  younger. 

Our  limits  do  not  permit  us  to  enter  into  a  discussion  of  Darwin's 
"  tidal  theory  "  of  satellite  formation,  which  may  be  regarded  as  in  a 
sense  supplementary  to  the  nebular  hypothesis ;  nor  can  we  more  than 
mention  Faye's  proposed  modification  of  it.  According  to  him,  the 
inner  planets  are  the  oldest. 

394.  Lockyer's  Meteoric  Hypothesis.  —  Within  the  last  two 
years  Mr.  Lockyer  has  vigorously  revived  a  theory  which  has 
been  from  time  to  time  suggested  before;  viz.,  that  all  the 
heavenly  bodies  in  their  present  state  are  mere  clouds  of 
meteors,  or  have  been  formed  by  the  condensation  of  such 
clouds ;  and  it  is  an  interesting  fact,  as  Professor  G.  H.  Dar- 
win has  recently  shown,  that  a  large  swarm  of  meteors,  in 
which  the  individuals  move  swiftly  in  all  directions,  would,  in 
the  long  run  and  as  a  whole,  behave  almost  exactly,  from  a 
mechanical  point  of  view,  in  the  same  way  as  one  of  Laplace's 
hypothetical  gaseous  nebulae.1 

1  This  is  not  very  strange,  after  all.  According  to  the  modern  "kinetic 
theory  of  gases  "  (Rolfe's  "Physics,"  page  157),  a  meteor  cloud  is  mechani- 


290  STARS,    STAR-CLUSTERS,   AND  NEBTTLJE.  [§  394 

The  spectroscopic  observations  upon  which  Mr.  Lockyer  rests  his 
attempted  demonstration  are  many  of  them  very  doubtful ;  but  that 
does  not  really  discredit  the  main  idea,  except  so  far  as  the  question 
of  the  origin  and  nature  of  the  light  of  the  heavenly  bodies  is  con- 
cerned. He  makes  the  light  in  all  cases  depend  upon  the  collisions 
between  the  meteors,  and  finds  in  the  spectra  of  the  heavenly  bodies 
evidence  of  the  presence  of  materials  with  which  we  are  familiar  in  the 
meteorites  which  fall  upon  the  earth's  surface.  These  identifications 
are  in  many  cases  questionable,  and  it  seems  much  more  likely  that 
the  luminosity  depends  to  a  great  degree  upon  other  than  mere 
mechanical  actions. 

395.  Stars,  Star-clusters,  and  Nebulae.  —  It  is  obvious  that 
the  nebular  hypothesis  in  all  its  forms  applies  to  the  explana- 
tion of  the  relations  of  these  different  classes  of  bodies  to 
each,  other.      In  fact,  Herschel,  appealing  only  to  the  "law 
of  continuity,"  had  concluded,  before  Laplace  published  his 
theory,  that  the  nebulae  develop  sometimes  into  clusters,  some- 
times into  double  or  multiple  stars,  and  sometimes  into  single 
stars.     He  showed  the  existence  in  the  sky  of  all  the  inter- 
mediate forms  between  the  nebula  and  the  finished  star.     For 
a  time,  about  forty  years  ago,  while  it  was  generally  believed 
that  -all  the  nebulas  were  only  star-clusters,  too  remote  to  be 
resolved  by  existing  telescopes,  his  views  fell  rather  into  abey- 
ance ;  but  they  regained  acceptance  in  their  essential  features 
when  the  spectroscope  demonstrated  the  substantial  difference 
between  gaseous  nebulae  and  the  star-clusters. 

396.  Conclusions  from  the  Theory  of  Heat.  —  Kant  and  La- 
place, as  Newcomb  says,  seem  to  have  reached  their  results  by 
reasoning  forwards.      Modern  science  comes  to  very  similar 

cally  just  the  same  thing  as  a  mass  of  gas  magnified.  The  kinetic  theory 
asserts  that  gas  is  only  a  swarm  of  minute  molecules,  the  peculiar  gaseous 
properties  depending  upon  the  collisions  of  these  molecules  with  each 
other  and  with  the  walls  of  the  enclosing  vessel.  Magnify  sufficiently  the 
molecules  and  the  distances  between  them,  and  you  have  a  meteoric  cloud. 


§  396]  AGE   OF   THE   SYSTEM.  291 

conclusions  by  working  backwards  from  the  present  state  of 
things. 

Many  circumstances  go  to  show  that  the  earth  was  once 
much  hotter  than  it  now  is.  As  we  penetrate  below  the  sur- 
face, the  temperature  rises  nearly  a  degree  (Fahrenheit)  for 
every  sixty  feet,  indicating  a  white  heat  at  the  depth  of  a  few 
miles ;  the  earth  at  present,  as  Sir  William  Thomson  says,  "  is 
in  the  condition  of  a  stone  that  has  been  in  the  fire  and  has 
cooled  at  the  surface." 

The  moon  bears  apparently  on  its  surface  the  marks  of  the 
most  intense  igneous  action,  but  seems  now  to  be  entirely 
chilled. 

The  planets,  so  far  as  we  can  make  out  with  the  telescope, 
exhibit  nothing  at  variance  with  the  view  that  they  were  once 
intensely  heated,  while  many  things  go  to  establish  it.  Jupi- 
ter and  Saturn,  Uranus  and  Neptune,  do  not  seem  yet  to  have 
cooled  off  to  anything  like  the  earth's  condition. 

As  to  the  sun,  we  have  in  it  a  body  continuously  pouring 
forth  an  absolutely  inconceivable  quantity  of  heat  without  any 
visible  source  of  supply.  As  has  been  explained  already  (Art. 
192),  the  only  rational  explanation  of  the  facts,  thus  far  pre- 
sented, is  that  which  makes  it  a  huge,  cloud-mantled  ball  of 
elastic  substance,  slowly  shrinking  under  its  own  central  grav- 
ity, and  thus  generating  heat.1  A  shrinkage  of  about  300  feet 
a  year  in  the  sun's  diameter  will  account  for  the  whole  annual 
output  of  radiant  heat  and  light. 

397.  Age  of  the  System.  —  Looking  backward,  then,  and 
trying  to  imagine  the  course  of  time  and  of  events  reversed, 
we  see  the  sun  growing  larger  and  larger,  until  at  last  it  has 

1  So  far  we  have  no  decisive  evidence  whether  the  sun  has  passed  its 
maximum  of  temperature  or  not.  Mr.  Lockyer  thinks  its  spectrum 
(resembling  as  it  does  that  of  Capella  and  the  stars  of  the  second  class) 
proves  that  it  is  now  on  the  downward  grade  and  growing  cooler;  but 
others  do  not  consider  the  evidence  conclusive. 


292  FUTURE  DURATION  OF  THE  SYSTEM.  [§  397 

expanded  to  a  huge  globe  that  fills  the  largest  orbit  of  our 
system.  How  long  ago  this  may  have  been,  we  cannot  state 
with  certainty.  If  we  could  assume  that  the  amount  of  heat 
yearly  radiated  by  the  solar  surface  had  remained  constantly 
the  same  through  all  those  ages,  and,  moreover,  that  all  the 
radiated  heat  came  solely  from  the  slow  contraction  of  the 
sun's  mass,  apart  from  any  considerable  original  capital  in 
the  form  of  a  high  initial  temperature,  and  without  any  re- 
enforcement  of  energy  from  outside  sources,  —  if  we  could 
assume  these  premises,  it  is  easy  to  show  that  the  sun's  past 
history  must  cover  about  15,000000  or  20,000000  years.  But 
such  assumptions  are  at  least  doubtful ;  and  if  we  discard 
them,  all  that  can  be  said  is  that  the  sun's  age  must  be 
greater,  and  probably  many  times  greater,  than  the  limit  we 
have  named. 

398.  Future  Duration  of  the  System.  —  Looking  forward, 
on  the  other  hand,  from  the  present  towards  the  future,  it  is 
easy  to  conclude  with  certainty  that  if  the  sun  continues  its 
present  rate  of  radiation  and  contraction,  and  receives  no  sub- 
sidies of   energy  from  without,  it  must,  within  5,000000  or 
10,000000  years,  become  so  dense  that  its  constitution  will  be 
radically  changed.     Its  temperature  will  fall  and  its  function 
as  a  sun  will  end.     Life  on  the  earth,  as  we  know  life,  will  be 
no  longer  possible  when  the  sun  has  become  a  dark,  rigid, 
frozen  globe.     At  least  this  is  the  inevitable  consequence  of 
what  now  seems  to  be  the  true  account  of  the  sun's  condition 
and  activity. 

399.  The  System  not   Eternal.  —  One  conclusion  seems  to 
be  clear :   That  the  present  system  of  stars   and   worlds   is 
not  an  eternal  one.     We  have  before  us  everywhere  evidence 
of  continuous,  irreversible  progress  from  a  definite  beginning 
towards  a  definite  end.     Scattered  particles  and  masses  are 
gathering  together  and  condensing,  so  that  the  great  grow  con- 


§  399]  THE   SYSTEM   NOT   ETERNAL.  293 

tinually  larger  by  capturing  and  absorbing  the  smaller.  At 
the  same  time  the  hot  bodies  are  losing  their  heat  and  distrib- 
uting it  to  the  colder  ones,  so  that  there  is  an  unremitting 
tendency  towards  a  uniform,  and  therefore  useless,  temperature 
throughout  our  whole  universe :  for  heat  is  available  as  energy 
(i.e.,  it  can  do  ivork)  only  when  it  can  pass  from  a  warmer 
body  to  a  colder  one.  The  continual  warming  up  of  cooler 
bodies  at  the  expense  of  hotter  ones  always  means  a  loss, 
therefore,  not  of  energy,  —  for  that  is  indestructible,  —  but  of 
available  energy.  To  use  the  ordinary  technical  term,  energy 
is  continually  "dissipated  "  by  the  processes  which  constitute 
and  maintain  life  on  the  universe.  This  dissipation  of  energy 
can  have  but  one  ultimate  result,  that  of  absolute  stagnation 
when  the  temperature  has  become  everywhere  the  same. 

If  we  carry  our  imagination  backwards,  we  reach  "  a  begin- 
ning of  things,"  which  has  no  intelligible  antecedent ;  if  for- 
wards, we  come  to  an  end  of  things  in  dead  stagnation.  That 
in  some  way  this  end  of  things  will  result  in  a  "  new  heavens 
and  a  new  earth  "  is,  of  course,  probable,  but  science  as  yet 
can  present  no  explanation  of  the  method. 


APPENDIX. 

CHAPTER   XIII. 

ASTRONOMICAL    INSTRUMENTS. 

THE  CELESTIAL  GLOBE. —  THE  TELESCOPE  :   SIMPLE,  ACHRO- 
MATIC,    AND     REFLECTING.  —  THE    EQUATORIAL.  —  THE 
FILAR     MICROMETER.  —  THE     TRANSIT     INSTRUMENT.  - 
THE   CLOCK  AND   CHRONOGRAPH. — THE  MERIDIAN   CIR- 
CLE.—  THE   SEXTANT. 

400,  The  Celestial  Globe.  —  The  celestial  globe  is  a  ball, 
usually  of  papier-mache",  upon  which  are  drawn  the  circles  of 
the  celestial  sphere  and  a  map  of  the  stars.  It  is  ordinarily 
mounted  in  a  framework  which  represents  the  horizon  and  the 
meridian,  in  the  manner  shown  in  Fig.  83. 

The  "horizon,"  HH'  in  the  figure,  is  usually  a  wooden 
ring  three  or  four  inches  wide  and  perhaps  three-quarters  of 
an  inch  thick,  directly  supported  by  the  pedestal.  It  carries 
upon  its  upper  surface  at  the  inner  edge  a  circle  marked  with 
degrees  for  measuring  the  azimuth  of  any  heavenly  body,  and 
outside  this  the  so-called  zodiacal  circles,  which  give  the  sun's 
longitude  and  the  equation  of  time  for  every  day  of  the  year. 

The  meridian  ring,  MM' ,  is  a  circular  ring  of  metal  which 
carries  the  bearings  upon  which  the  globe  revolves.  Things 
are  so  arranged,  or  ought  to  be,  that  the  mathematical  axis 
of  the  globe  is  exactly  in  the  same  plane  as  the  graduated  face 

295 


296 


APPENDIX. 


[§400 


of  the  ring,  which  is  divided  into  degrees.  The  meridian  ring 
is  held  underneath  the  globe  by  a  support,  with  a  clamp  which 
enables  us  to  fix  it  securely  in  any  desired  position. 

The  surface  of  the  globe  is  marked  first  with  the  celestial 
equator,  next  with  the  ecliptic,  crossing  the  equator  at  an 


FIG.  83. —The  Celestial  Globe. 

angle  of  23  J°  at  F(as  the  figure  is  drawn,  V  happens  to  be  the 
autumnal  equinox,  not  the  vernal),  and  each  of  these  circles  is 
divided  into  degrees.  The  equinoctial  and  solstitial  colures 
are  also  always  represented.  As  to  the  other  circles,  usage 
differs.  The  ordinary  way  at  present  is  to  mark  the  globe 
with  twenty-four  hour-circles  15°  apart  (the  colures,  Art.  117, 
being  four  of  them),  and  with  parallels  of  declination  10° 


§  400]  TO  RECTIFY   A   GLOBE.  297 

apart.     On  the  surface  of  the  globe  are  plotted  the  positions 
of  the  stars  and  the  outlines  of  the  constellations. 

It  is  perhaps  worth  noting  that  many  of  the  spirited  figures  of  the 
constellations  upon  our  present  globes  are  copied  from  designs  drawn 
by  Albert  Diirer  for  a  star-map  published  in  his  time. 

The  Hour-index  is  a  small  circle  of  thin  metal,  about  four 
inches  in  diameter,  which  is  fitted  to  the  northern  pole  of  the 
globe  with  a  stiffish  friction,  so  that  it  can  be  set  like  the 
hands  of  a  clock,  and  when  once  set  will  turn  with  the  globe 
without  shifting. 

401.  To  rectify  a  Globe,  —  i.e.,  to  set  it  so  as  to  show  the 
aspect  of  the  heavens  at  any  time :  — 

(1)  Elevate  the  north  pole  of  the  globe  to  an  angle  equal 
to  the   observer's   latitude   by  means   of  the   graduation  on 
the  meridian  ring,  and  clamp  the  ring  securely. 

(2)  Look  up  the  day  of  the  month  on  the  horizon  of  the 
globe,  and  opposite  to  the  day  find  on  the  zodiacal  circle  the 
sun's  longitude  for  that  day. 

(3)  On  the  ecliptic  (upon  the  surface  of  the  globe)  find 
the  degree  of  longitude  thus  indicated,  and  bring  it  to  the 
graduated  face  of  the  meridian  ring.     The  globe  is  thus  set  to 
correspond  to  apparent  noon  of  the  day  in  question. 

It  may  be  well  to  mark  the  place  of  the  sun  temporarily  with  a  bit 
of  paper  gummed  on  at  the  proper  place  in  the  ecliptic.  It  can  easily 
be  wiped  off  after  using. 

(4)  Hold  the  globe  fast,  so  as  to  keep  the  place  of  the  sun 
exactly  on  the  meridian,  and  turn  the  hour-index  until  it  shows 
at  the  edge  of  the  meridian  ring  the  mean  time  of  apparent 
noon  (i.e.,  12h  ±  the  equation  of  time  given  on  the  wooden 
horizon  for  the  day  in  question). 

If  standard  time  is  used,  the  hour-index  must  be  set  to  the  standard 
time  for  apparent  noon  instead  of  the  local  mean  time. 


298  APPENDIX.  [§  401 

(5)  Finally,  turn  the  globe  upon  its  axis  until  the  hour- 
index  shows  at  the  meridian  the  hour  for  which  it  is  to  be 
set.  The  globe  will  then  represent  the  true  aspect  of  the 
heavens  at  that  time. 

The  positions  of  the  moon  and  planets  are  not  given  by  this  opera- 
tion, since  they  have  no  fixed  places  in  the  sky,  and  therefore  cannot 
be  put  in  by  the  globe-maker.  If  one  wants  them  represented,  he 
must  look  up  their  right  ascensions  and  declinations  in  some  almanac, 
and  mark  the  proper  places  on  the  globe  with  bits  of  wax  or  paper. 


TELESCOPES. 

402.  Telescopes  are  of  two  kinds,  —  refracting  and  reflecting. 
The  refractor  was  first  invented,  early  in  the  seventeenth 

century,  and  is  much  more  used,  but  the  largest  instruments 
ever  made  dfre  reflectors.  In  both,  the  fundamental  principle 
is  the  same.  The  large  lens  of  the  instrument  (or  else  its 
concave  mirror)  forms  a  real  image  of  the  object  looked  at, 
and  this  image  is  then  examined  and  magnified  by  the  eye- 
piece, which  in  principle  is  only  a  magnifying-glass. 

In  the  form  of  instrument,  however,  which  was  originally  devised 
by  Galileo  and  is  still  used  as  the  "  opera-glass,"  the  rays  from  the 
object-glass  are  intercepted,  and  brought  to  parallelism,  by  the  concave 
lens  which  serves  as  an  eye-glass,  before  they  form  the  image.  Tele- 
scopes of  this  construction  are  never  made  of  much  power,  being 
inconvenient  on  account  of  the  smallness  of  the  field  of  view. 

403.  The    Simple    Refracting    Telescope.  —  This    consists 
essentially,  as  shown  in  Fig.  84,  of  two  convex  lenses  :  one, 
the  object-glass  A,  of  large  size  and  long  focus ;  the  other,  the 
eye-glass  B,  of  short  focus,  —  the  two  being  set  at  a  distance 
nearly  equal  to  the  sum  of  their  focal  lengths.     Recalling  the 
optical  principles  relating  to  the  formation  of  images  by  lenses, 
we  see  that  if  the  instrument  is  pointed  towards  the  moon,  for 
instance,  all  the  rays  that  strike  the  object-glass  from  the  top 


§  403]  MAGNIFYING   POWER.  299 

of  the  crescent  will  be  collected  to  a  focus  at  a,  while  those 
from  the  bottom  will  come  to  a  focus  at  b ;  and  similarly  with 
rays  from  the  other  points  on  the  surface  of  the  moon.  We 
shall,  therefore,  get  in  the  "focal  plane  "  of  the  object-glass  a 
small  inverted  "image"  of  the  moon.  The  image  is  a  real 


FlQ.  84.  — The  Simple  Refracting  Telescope. 

one;  i.e.,  the  rays  really  meet  at  the  focal  points,  so  that  if  we 
insert  a  photographic  plate  in  the  focal  plane  at  ab  and  prop- 
erly expose  it,  we  shall  get  a  picture  of  the  object.  The  size 
of  the  picture  will  depend  upon  the  apparent  angular  diameter 
of  the  object  and  the  distance  from  the  object-glass  to  the 
image  ab. 

If  the  focal  length  of  the  lens  A  is  ten  feet,  then  the  image  of  the 
moon  will  be  a  little  more  than  one  inch  in  diameter. 

404.  Magnifying  Power.  —  If  we  use  the  naked  .eye,  we 
cannot  see  the  image  distinctly  from  a  distance  much  less  than 
a  foot,  but  if  we  use  a  magnifying  lens  of,  say,  one  inch  focus, 
we  can  view  it  from  a  distance  of  only  an  inch,  and  it  will 
look  correspondingly  larger.  Without  stopping  to  prove  the 
principle,  we  may  say  that  the  magnifying  power  is  simply 
equal  to  the  quotient  obtained  by  dividing  the  focal  length  of  the 
object-glass  by  that  of  the  eye-lens. 

It  is  to  be  noted,  however,  that  a  magnifying  power  of  unity  is 
sometimes  spoken  of  as  no  magnifying  power  at  all,  since  the  image 
appears  of  the  same  size  as  the  object. 

The  magnifying  power  of  a  telescope  is  changed  at  pleasure  by 
simply  interchanging  the  eye-pieces,  of  which  every  telescope  of  any 
pretensions  always  has  a  considerable  stock,  giving  various  powers. 


300  APPENDIX.  [§  405 

405,  Brightness  of  the  Image.  —  This  depends  not  upon  the 
focal  length  of  the   object-glass,  but  upon  its  diameter;  or, 
more  strictly,  its  area.     If  we  estimate  the  diameter  of  the 
pupil  of  the  eye  at  one-fifth  of  an  inch,  as  it  is  usually  reck- 
oned, then  (neglecting  the  loss  from  want  of  perfect  transpar- 
ency in  the  lenses)  a  telescope  one  inch  in  diameter  collects 
into  the  image  of  a  star  25  times  as  much  light  as  the  naked 
eye  receives ;  and  the  great  Lick  telescope  of  36  inches  in 
diameter,  32,400  times  as  much,  or  about  30,000  after  allow- 
ing for  the  losses.     The  amount  of  light  is  proportional  to  the 
square  of  the  diameter  of  the  object-glass. 

The  apparent  brightness  of  an  object  which,  like  the  moon  or 
a  planet,  shows  a  disc,  is  not,  however,  increased  in  any  such 
ratio,  because  the  light  gathered  by  the  object-glass  is  spread 
out  by  the  magnifying  power  of  the  eye-piece.  But  the  total 
quantity  of  light  in  the  image  of  the  object  greatly  exceeds 
that  which  is  available  for  vision  with  the  naked  eye,  and 
objects  which,  like  the  stars,  are  mere  luminous  points,  have 
their  brightness  immensely  increased,  so  that  with  the  tele- 
scope millions  otherwise  invisible  are  brought  to  light.  With 
the  telescope,  also,  the  brighter  stars  are  easily  seen  in  the 
daytime. 

406.  The  Achromatic   Telescope.  —  A    single    lens    cannot 
bring  the  rays  which  emanate  from  a  single  point  in  the  object 
to  any  exact  focus,  since  the  rays  of  each  different  color  are 
differently  refracted,  —  the  blue  more  than  the  green,  and  this 
more  than  the  red.     In  consequence  of  this  so-called  "  chro- 
matic aberration,"  the  simple  refracting  telescope  is  a  very 
poor1  instrument. 

1  By  making  it  extremely  long  in  proportion  to  its  diameter,  the  indis- 
tinctness of  the  image  is  considerably  diminished,  and  in  the  middle  of  the 
seventeenth  century  instruments  more  than  100  feet  in  length  were  used 
by  Huyghens  and  others.  Saturn's  rings  and  several  of  his  satellites  were 
discovered  with  instruments  of  this  kind. 


§  406]  ACHROMATISM  NOT  PERFECT.  301 

About  1760,  it  was  discovered  in  England  that  by  making 
the  object-glass  of  two  or  more  lenses  of  different  kinds  of 
glass,  the  chromatic  aberration  can  be  nearly  corrected.  Object- 
glasses  so  made  —  none  others  are  now  in  common  use  —  are 
called  achromatic.  In  practice,  only  two  lenses  are  ordinarily 
used  in  the  construction  of  an  astronomical  glass,  —  a  convex 
of  crown  glass,  and  a  concave  of  flint  glass,  the  curves  of  the 
two  lenses  and  the  distances  between  them  being  so  chosen  as 
to  give  the  most  perfect  possible  correction  of  the  "  spherical " 
aberration  ("  Physics,"  p.  363)  as  well  as  of  the  chromatic. 

407.  Achromatism  not  Perfect.  —  It  is  not  possible  with  the 
kinds  of  glass  hitherto  available  to  obtain  a  perfect  correction 
of  color.     Even  the  best  achromatic  telescopes  show  a  purple 
halo  around  the  image  of  a  bright  star,  which,  though  usually 
regarded  as  "very  beautiful"  by  tyros,  seriously  injures  the 
definition,  and  is  especially  obnoxious  in  large  instruments. 

This  imperfection  of  achromatism  makes  it  impossible  to  get  satis- 
factory photographs  with  an  ordinary  object-glass,  corrected  for  vision. 
An  instrument  for  photography  must  have  an  object-glass  specially 
corrected  for  the  purpose,  since  the  rays  most  efficient  in  impressing 
the  image  upon  the  photographic  plate  are  the  blue  and  violet  rays, 
which  in  the  ordinary  object-glass  are  left  to  wander  very  wildly. 

Much  is  hoped  from  the  new  kinds  of  glass  now  being  made  for 
optical  purposes  at  Jena,  Germany,  as  the  results  of  the  experiments 
conducted  by  Professor  Abbe  at  the  expense  of  the  German  govern- 
ment. Though  the  new  glass  is  especially  intended  for  use  in  the  con- 
struction of  microscopes,  a  few  telescope  lenses  from  three  to  six  inches 
in  diameter  have  been  already  made  with  it,  which  appear  to  be  nearly 
perfect  in  their  color  correction. 

408.  Diffraction  and  Spurious  Discs.  —  Even  if  a  lens  were 
absolutely  perfect  as  regards  the   correction  of  aberrations, 
both  spherical  and  chromatic,  it  would  still  be  unable  to  give 
vision  absolutely  distinct.      Since  light  consists  of  waves  of 
finite  length,  the  image  of  a  luminous  point  can  never  be  also 


302  APPENDIX.  [§  408 

a  point,  but  must  of  mathematical  necessity  be  a  disc  of  finite 
diameter  surrounded  by  a  series  of  'diffraction'  rings.  The 
diameter  of  the  "'spurious  disc"  of  a  star,  as  it  is  called, 
varies  inversely  with  the  diameter  of  the  object-glass  :  the 
larger  the  telescope,  the  smaller  the  image  of  a  star  with  a 
given  magnifying  power. 

With  a  good  telescope  and  a  power  of  about  30  to  the  inch  of  aper- 
ture (120  for  a  4-inch  telescope)  the  image  of  a  star,  when  the  air  is 
steady  (a  condition  unfortunately  seldom  fulfilled),  should  be  a  clean, 
round  disc,  with  a  bright  ring  around  it,  separated  from  the  disc  by 
a  clear  black  space.  According  to  Dawes,  the  disc  of  a  star  with  a 
4^-inch  telescope  should  be  about  1"  in  diameter;  with  a  9-inch  instru- 
ment 0".5,  and  |"  for  a  36-inch  glass. 

409.  Eye-pieces.  —  For  some  purposes  the  simple  convex 
lens  is  the  best  "  eye-piece  "  possible  ;  but  it  performs  well 
only  for  a  small  object,  like  a  close  double  star,  placed  exactly 

Huyghenian  in     the     C6Iltre    °f     the    field    °f 

view.  Generally,  therefore,  we 
employ  "  eye-pieces  "  composed 
of  two  or  more  lenses,  which 
give  a  larger  field  of  view  than 
a  single  lens,  and  define  satis- 

FIG.  85.  —  Telescope  Eye-pieces. 

tactorily  over  the  whole  extent 

of  the  field.  They  fall  into  two  general  classes,  the  positive 
and  the  negative. 

The  positive  eye-pieces  are  much  more  generally  useful.  They  act 
as  simple  magnifying-glasses,  and  can  be  taken  out  of  the  telescope 
and  used  as  hand-magnifiers  if  desired.  The  image  of  the  object 
formed  by  the  object-glass  lies  outside  of  this  kind  of  eye-piece,  between 
it  and  the  object-glass. 

In  the  negative  eye-piece,  on  the  other  hand,  the  rays  from  the 
object-glass  are  intercepted  by  the  so-called  "  field-lens  "  before  reach- 
ing the  focus,  and  the  image  is  formed  between  the  two  lenses  of  the 
eye-piece.  It  cannot  therefore  be  used  as  a  hand-magnifier. 

Fig.  85  shows  the  two  most  usual  forms  of  eye-piece. 


§  409]  THE  REFLECTING  TELESCOPE.  303 

These  eye-pieces  show  the  object  in  an  inverted  position; 
but  this  is  of  no  importance  as  regards  astronomical  obser- 
vations. 

410.  Reticle. — When  the   telescope   is   used   for   pointing 
upon  an  object,  as  it  is  in  most  astronomical  instruments,  it 
must  be  provided  with  a  '  reticle '  of  some  sort.     The  simplest 
form  is  a  metallic  frame  with  spider  lines  stretched  across  it, 
the  intersection  of  the  spider  lines  being  the  point  of  reference. 
This  reticle  is  placed  not  at  or  near  the  object-glass,  as  is  often 
supposed,  but -MI  its  focal  plane,  as  ab  in  Fig.  84.     Sometimes  a 
glass  plate  with  fine  lines  ruled  upon  it  is  used  instead  of 
spider  lines.     Some  provision  must  be  made  for  illuminating 
the  lines,  or  "  wires,"  as  they  are  usually  called,  by  reflecting 
into  the  instrument  a  faint  light  from  a  lamp  suitably  placed. 

411.  The   Reflecting   Telescope.  —  About  1670,   when  the 
chromatic  aberration  of  refractors  first  came  to  be  understood 
(in  consequence  of  Newton's  discovery  of  the  "  decomposition 
of  light "),  the  reflecting  telescope  was  invented.     For  nearly 
150  years  it  held  its  place  as  the  chief  instrument  for  star- 
gazing, until  about  1820,  when  large  achromatics  began  to  be 
made.     There  are  several  varieties  of  reflecting  telescope,  dif- 
fering in  the  way  in  which  the  image  formed  by  the  mirror  is 
brought  within  reach  of  the  magnifying  eye-piece. 

Until  about  1870,  the  large  mirror  (technically  "  speculum ") 
was  always  made  of  speculum  metal,  a  composition  of  copper 
and  tin.  It  is  now  usually  made  of  glass,  silvered  on  the  front 
by  a  chemical  process.  When  new,  these  silvered  films  reflect 
much  more  light  than  the  old  speculum  metal :  they  tarnish 
rather  easily,  but  fortunately  can  be  easily  renewed. 

412.  Large  Telescopes.  —  The  largest  telescopes  ever  made  have 
been  reflectors.     At  the  head  stands  the  enormous  instrument  of  Lord 
Rosse  of  Birr  Castle,  Ireland,  six  feet  in  diameter  and  sixty  feet  long, 


304  APPENDIX.  [§  412 

made  in  1842,  and  still  used.  Next  in  size,  but  probably  superior  in 
power,  comes  the  five-foot  silver-on-glass  reflector  of  Mr.  Common,  at 
Baling,  England,  completed  in  1889 ;  and  then  follow  a  number  (four 
or  five)  of  four-foot  telescopes,  —  that  of  Herschel  (erected  in  1789,  but 
long  ago  dismantled)  being  the  first,  while  the  great  instrument  at 
Melbourne  is  the  only  instrument  of  this  size  now  in  active  use. 

Of  the  refractors,  the  largest  is  that  of  the  Lick  Observatory  (see 
frontispiece),  which  has  an  aperture  of  36  inches  and  a  length  of 
nearly  60  feet.  The  next  in  size  is  that  of  Pulkowa,  30  inches  in  diam- 
eter, and  this  is  nearly  equalled  by  the  great  telescope  at  Nice,  with 
an  aperture  of  29£  inches.  Then  come  the  Vienna  telescope,  27 
inches ;  the  two  telescopes  at  Washington  and  the  University  of  Vir- 
ginia, 26^  inches  aperture;  the  Newhall  telescope  (just  presented  to 
the  University  of  Cambridge,  England),  25  inches ;  and  the  Princeton 
telescope,  23  inches.  These  are  at  present  (1890)  all  the  refractors 
which  have  an  aperture  exceeding  20  inches,  but  a  number  of  others 
are  now  under  construction.  All  these  large  object-glasses  were  made 
by  the  Clarks  of  Cambridge  (U.S.),  excepting  those  at  Nice,  Vienna, 
and  Cambridge  (England). 

413.   Relative  Advantages  of  Reflectors  and   Refractors. — 

There  is  no  little  discussion  on  this  point,  each  form  of  instrument 
having  its  earnest  partisans. 

In  favor  of  the  reflector  we  have  Jirst,  its  comparative  ease  of  con- 
struction and  cheapness,  since  there  is  but  one  surface  to  grind  and 
polish,  as  against  four  in  an  achromatic  object-glass ;  second,  the  fact 
that  reflectors  can  be  made  larger  than  refractors ;  third,  the  reflector 
is  absolutely  achromatic. 

On  the  other  hand,  a  refractor  gives  a  much  brighter  image  than  a 
reflector  of  the  same  size;  it  also  generally  defines  much  better, 
because,  for  optical  reasons  into  which  we  cannot  enter  here,  any 
slight  distortion  or  malformation  of  the  speculum  of  a  reflector  dam- 
ages the  image  many  times  more  than  the  same  amount  of  distortion 
of  an  object-glass.  Then  a  lens  hardly  deteriorates  at  all  with  age, 
while  a  speculum  soon  tarnishes,  and  must  be  re-silvered  or  re-polished 
every  few  years. 

As  a  rule,  also,  refractors  are  lighter  and  more  convenient  than 
reflectors  of  equal  power. 


§414] 


MOUNTING   OF  A  TELESCOPE. 


305 


414.  Mounting  of  a  Telescope,  —  the  Equatorial.  —  A  tele- 
scope, however  excellent  optically,  is  not  good  for  much  unless 
firmly  and  conveniently  mounted.1 

At  present  some  form  of  equatorial  mounting  is  practically 
universal.  Fig.  86  represents  schematically  the  ordinary  ar- 
rangement of  the  instrument.  Its  essential  feature  is  that  its 
"principal  axis"  (i.e.,  the  one  which  turns  in  fixed  bearings 
attached  to  the  pier,  and  is  called  the  polar  aocis)  is  placed  par- 
allel to  the  earth's  axis,  pointing  to 
the  celestial  pole,  so  that  the  circle 
Ht  attached  to  it,  is  parallel  to  the 
celestial  equator.  This  circle  is 
sometimes  called  the  hour-circle, 
sometimes  the  right-ascension  circle. 
At  the  extremity  of  the  polar  axis  a 
"  sleeve  "  is  fastened,  which  carries 
within  it  the  declination  axis  D, 
and  to  this  declination  axis  is  at- 
tached the  telescope  tube  T,  and 
also  the  declination  circle  C. 

The  advantages  of  this  mount- 
ing are  very  great.  In  the  first 
place,  when  the  telescope  is  once 
pointed  upon  an  object,  it  is  not 
necessary  to  move  the  declination  axis  at  all  in  order  to  keep 
the  object  in  the  field,  but  only  to  turn  the  polar  axis  with  a 
perfectly  uniform  motion,  which  motion  can  be,  and  usually  is, 
given  by  clock-work  (not  shown  in  the  figure). 

In  the  next  place,  it  is  very  easy  to  find  an  object  even  if 


FIG.  86.  —  The  Equatorial. 


1  We  may  add  that  it  must,  of  course,  be  mounted  where  it  can  be 
pointed  directly  at  the  stars,  without  any  intervening  window-glass  be- 
tween it  and  the  object.  We  have  known  purchasers  of  telescopes  to 
complain  bitterly  because  they  could  not  see  Saturn  well  through  a  closed 
window. 


306 


APPENDIX. 


[§414 


invisible  to  the  eye  (like  a  faint  comet,  or  a  star  in  the  day- 
time), provided  we  know  its  right  ascension  and  declination, 
and  have  the  sidereal  time,  —  a  sidereal  clock  or  chronometer 
being  an  indispensable  accessory  of  the  instrument. 

The  frontispiece  shows  the  actual  mounting  of  the  Lick  telescope. 
Fig.  71,  Art.  337,  represents  another  form  of  equatorial  mounting, 
which  has  been  adopted  for  the  instruments  of  the  photographic 
campaign. 

415.  The  Micrometer.  —  This  is  an  instrument  for  measur- 
ing small  angles,  usually  not  exceeding  15'  or  20'.     Various 

kinds  are  employed,  all  of 
them  small  pieces  of  ap- 
paratus, which,  when  used, 
are  secured  to  the  eye-end 
of  a  telescope.  The  most 
common  is  the  parallel- 
wire  micrometer,  which  is 
a  pair  of  parallel  spider 
threads,  one  or  both  of 
which  can  be  moved  with 
a  fine  screw  with  a  grad- 
uated head,  so  that  the 
distance  between  the  two 
1  wires J  can  be  varied  at 
pleasure,  and  then  "  read 
off"  by  looking  at  the 
micrometer  head.  Fig.  87 
represents  such  an  instru- 
ment attached  to  a  telescope :  the  spider  threads  are  in  the 
box  BB,  and  are  viewed  through  the  eye-piece. 

416.  The  Transit  Instrument  (Fig.  88).  — This  consists  of 
a  telescope  carrying  at  the  eye-end  a  reticle,  and  mounted  on 
a  stiff  axis  with  pivots  that  are  perfectly  true.     They  turn  in 


Fio.  87.  —  The  Filar  Position  Micrometer. 


§416] 


THE  ASTRONOMICAL  CLOCK,   ETC. 


307 


Y's,  which  are  firmly  set  upon  some  sort  of  framework  or  on 
the  top  of  solid  piers,  and  so  placed  that  the  axis  will  be  ex- 
actly east  and  west  and  precisely  level.  When  the  telescope 
is  turned  on  its  axis,  the  mid- 
dle wire  of  the  reticle,  if 
everything  is  correctly  ad- 
justed, will  follow  the  celes- 
tial meridian,  and  whenever  a 
star  crosses  the  wire,  we  know 
that  it  is  exactly  on  the  me- 
ridian. Instead  of  a  single 
wire,  the  reticle  generally  con- 
tains a  number  of  wires 
equally  spaced,  as  shown  in 
Fig.  89.  The  object  is  then 
observed  upon  each  of  the 
wires,  and  the  mean  of  the 
observations  is  taken  as  giv- 
ing the  moment  when  the  star  crossed  the  middle  wire. 

A  delicate  spirit-level,  to  be  placed 
on  the  pivots  and  test  the  horizon- 
tality  of  the  axis,  is  an  indispensable 
accessory. 

So  far  as  the  theory  of  the  instru- 
ment is  concerned,  a  graduated  circle 
is  not  essential ;  but  practically  it  is 
necessary  to  have  one  attached  to 
the  axis  in  order  to  enable  the  ob- 
server to  set  for  a  star  in  preparing 
for  the  observation. 


FIG.  88.  —  The  Transit  Instrument. 


FIG.  89.  — Reticle  of  the  Transit 
Instrument. 


417.  The  Astronomical  Clock,  Chronometer,  and  Chrono- 
graph. —  A  good  timepiece  is  an  essential  adjunct  of  the  tran- 
sit instrument,  and  equally  so  of  most  other  astronomical 
instruments.  The  invention  of  the  pendulum  clock  by  Huy- 


308  APPENDIX.  [§  417 

ghens  was  almost  as  important  an  event  in  the  history  of 
practical  astronomy  as  that  of  the  telescope  itself. 

The  astronomical  clock  differs  in  no  essential  respect  from 
any  other,  except  that  it  is  made  with  extreme  care,  and  has  a 
"  compensated  "  pendulum  so  constructed  that  the  rate  of  the 
clock  will  not  be  affected  by  changes  of  temperature.  It  is 
almost  invariably  made  to  beat  seconds,  and  usually  has  its 
face  divided  into  twenty-four  hours  instead  of  twelve. 

Excellence  in  a  clock  consists  essentially  in  the  constancy  of 
its  'rate' ;  i.e.,  it  should  gain  or  lose  precisely  the  same  amount 
each  day,  and  as  a  matter  of  convenience  the  daily  rate  should 
be  small,  not  to  exceed  a  second  or  two.  The  rate  is  adjusted 
by  slightly  raising  or  lowering  the  pendulum  bob,  or  putting 
little  weights  upon  a  small  shelf  attached  to  the  rod ;  —  the 
'  error/  when  necessary,  by  simply  setting  the  hands. 

The  error  of  a  timepiece  is  the  difference  between  the  time  shown 
by  the  clock-face  and  the  true  time  at  the  moment ;  the  rate  is  the 
amount  it  gains  or  loses  in  twenty-four  hours. 

The  chronometer  is  simply  a  carefully  made  watch,  and  has 
the  advantage  of  portability,  though  in  'accuracy  it  cannot 
quite  compete  with  a  well-made  clock. 

Formerly  transit-instrument  observations  were  made  by  sim- 
ply noting  with  eye  and  ear  the  time  indicated  by  the  clock  at 
the  moment  when  the  star  observed  was  crossing  the  wire  or 
reticle.  A  skilful  observer  can  do  this  within  about  a  tenth 
of  a  second.  At  present  the  observer  usually  presses  a  tele- 
graph-key at  the  moment  of  the  transit,  and  so  telegraphs 
the  instant  to  an  instrument  called  a  "chronograph"  which 
makes  a  permanent  record  of  the  observation  upon  a  sheet 
of  paper,  —  thus  making  the  observation  much  more  accurate 
as  well  as  easier.  (For  the  description  of  the  chronograph, 
see  General  Astronomy,  Art.  56.) 

418.  The  Meridian  Circle.  —  In  many  respects  this  is  the 
fundamental  instrument  of  a  working  observatory.  It  is 


§418] 


THE  MERIDIAN   CIRCLE. 


309 


simply  the  transit  instrument  plus  a  finely  graduated   circle 

or  circles  attached  to  the  axis,  and  provided  with  microscopes 

for   reading  the  graduation  with  precision.     In  the  accurate 

construction  of  the  pivots 

of  the  instrument  and  of 

the     circles,    with    their 

graduation,  the  utmost  re- 

sources of  the  mechanical 

art   are   taxed.      Fig.   90 

shows  the  instrument  in 

principle.      Fig.   91   is  a 

small  meridian  circle,  as 

actually  constructed,  with 

a  four-inch  telescope  and 

twenty-four-inch  circles. 

Its  main  purpose  is  to 
determine  the  right  ascen- 
sion and  declination  of 
objects  as  they  cross  the 
meridian.  The  declination  is  determined  by  measuring  how 
many  degrees  the  object  is  north  or  south  of  the  celestial  equa- 
tor at  the  moment  of  transit.  The  "  circle-reading  "  for  the 
equator  must  first  be  determined  as  a  zero  point;  and  this  is 
done  by  observing  a  star  near  the  pole  and  getting  the  circle- 
reading  as  it  crosses  the  meridian  above  the  pole,  and  twelve 
hours  later,  when  it  crosses  again  below  it.  The  mean  of  these 
two  readings,  corrected  for  refraction,  will  be  the  circle-reading 
for  the  pole,  or  the  polar  point,  which  is,  of  course,  just  90° 
from  the  equatorial  zero  point. 

419.  The  Nadir  Point.  —  To  get  the  latitude  of  the  observer 
with  this  instrument  (Art.  81),  it  is  necessary  also  to  have  the. 
nadir  point  as  a  zero;  i.e.,  the  circle-reading  which  corresponds 
to  the  vertical  position  of  the  telescope.  This  point  is  found 
by  pointing  the  telescope  down  towards  a  basin  of  mercury 


F'°'  90'  ~  Tbe  Merld""1  oircle 


310 


APPENDIX. 


[§419 


beneath  it,  and  setting  it  so  that  the  image  of  the  east  and 
west  wire  in  the  reticle  coincides  with  itself.  Then  the  tele- 
scope will  be  exactly  vertical.  The  horizontal  point  is  just 
90°  from  the  nadir  point,  and  the  difference  between  the 


FIG.  91.  — A  Meridian  Circle. 


(north)  horizontal  point  and  the  polar  point  is  the  latitude  of 
the  observatory. 

Obviously  the  instrument  can  also  be  used  as  a  simple  tran- 
sit instrument  in  connection  with  a  clock,  so  that  (Art.  99)  the 


419] 


THE  SEXTANT. 


311 


observer  can  determine  both  the  right  ascension  and  declination 
of  any  object  which  is  visible  when  it  crosses  the  meridian. 

420.  The  Sextant.  —  All  the  instruments  so  far  mentioned, 
except  the  chronometer,  require  firmly  fixed  supports,  and  are, 
therefore,  useless  at  sea.  The  sextant  is  the  only  instrument 
for  measurement  upon  which  the  mariner  can  rely.  By  means 
of  it  he  can  measure  the  angular  distance  between  any  two 
points  (as,  for  instance,  the  sun  and  the  visible  horizon),  not 

JM 
8 


S' 


FIG.  92.  — The  Sextant. 

by  pointing  first  on  one  and  afterwards  on  the  other,  but  by 
sighting  them  both  simultaneously  and  in  apparent  coincidence. 
This  observation  can  be  accurately  made  even  if  he  has  no 
stable  footing,  but  is  swinging  about  on  the  deck  of  a  vessel. 
Fig.  92  represents  the  instrument.  For  a  detailed  description 
and  explanation,  see  General  Astronomy,  Arts.  76-80. 

421.   Use  of  the  Instrument. — The  principal  use  of  the  in- 
strument is  in  measuring  the  altitude  of  the  sun.     At  sea,  an 


312  APPENDIX.  [§  421 

observer  holding  the  instrument  in  his  right  hand,  and  keep- 
ing the  plane  of  the  arc  vertical,  looks  directly  towards  the 
visible  horizon  through  the  horizon-glass,  H,  at  the  point  under 
the  sun.  Then  by  moving  the  index,  N,  with  his  left  hand, 
he  inclines  the  index  mirror  upward,  until  he  sees  the  re- 
flected image  of  the  sun,  and  the  lower  edge  of  this  image  is 
brought  to  touch  the  horizon-line.  The  reading  of  the  gradu- 
ation, after  due  correction  for  refraction,  etc.,  gives  the  sun's 
true  altitude  at  the  moment.  If  the  observation  is  made  near 
noon,  for  the  purpose  of  determining  the  latitude,  it  will  not 
be  necessary  to  read  the  chronometer  at  the  same .  time.  If, 
however,  the  observation  is  made  for  the  purpose  of  determin- 
ing the  longitude  (Art.  497),  the  instant  of  observation,  as 
shown  by  the  chronometer,  must  be  carefully  noted. 

The  skilful  use  of  the  sextant  requires  considerable  dexterity, 
and  from  the  small  size  of  the  telescope,  the  angles  measured 
are  less  precisely  measured  than  with  large  fixed  instruments ; 
but  the  portability  of  the  instrument  and  its  applicability  at 
sea  render  it  absolutely  invaluable.  It  was  invented  by 
Gregory,  of  Philadelphia,  in  1730. 


422]  HOUR-ANGLE  AND   TIME.  313 


CHAPTER   XIV. 

MISCELLANEOUS. 

HOUR-ANGLE  AND  TIME. — TWILIGHT. — DETERMINATION 
OF  LATITUDE.  —  SHIP'S  PLACE  AT  SEA.  —  FINDING  THE 
FORM  OF  THE  EARTH'S  ORBIT.  —  THE  ELLIPSE.  —  ILLUS- 
TRATIONS OF  KEPLER'S  THIRD  LAW.  —  THE  EQUATION 

OF  LIGHT  AND  THE  SUN'S  DISTANCE. — ABERRATION  OF 
LIGHT.  —  DE  L'ISLE'S  METHOD  OF  GETTING  THE  SOLAR 
PARALLAX  FROM  THE  TRANSIT  OF  VENUS.  —  THE 
CONIC  SECTIONS.  —  STELLAR  PARALLAX. — THE  SLIT- 
LESS  SPECTROSCOPE. 

422.  Hour-angle  and  Time  (supplementary  to  Arts.  89-91). 
—  There  is  another  way  of  looking  at  the  matter  of  time, 
which  has  great  advantages.  If  we  face  towards  the  north 
pole  and  consider  the  star  ra  (Fig.  93)  as  carried  at  the  end 
of  the  arc  mP  of  the  hour-circle,  which  connects  it  to  the 
pole,  we  may  regard  this  arc  as  a  sort  of  clock-hand ;  and  if 
we  produce  it  to  the  celestial  equator  and  mark  off  the  equa- 
tor into  15°  spaces,  or  '  hours/  the  angle  QPm,  or  the  arc  Q  Y, 
will  measure  the  time  which  has  elapsed  since  m  was  on  the 
meridian  PQ.  The  angle  mPQ  is  called  the  Iwur-angle  of  the 
star  w.  It  is  the  angle  at  the  pole  between  the  meridian  and 
the  hour-circle  which  passes  through  the  body. 

Having  now  this  definition  of  the  hour-angle,  we  may  define 
sidereal  time  (Art.  91)  at  any  moment  as  the  hour-angle  of  the 
vernal  equinox  at  that  moment.  In  the  same  way,  the  apparent 
solar  time  (Art.  88)  is  the  hour-angle  of  the  sun's  centre ;  the 


314 


APPENDIX. 


[§422 


FIG.  93.  —  Hour-Angle. 


mean  solar  time  (Art.  89)  is  the  hour-angle  of  a  fictitious  sun 
which  moves  around  the  heavens  uniformly,  once  a  year,  in 

the  equator,  keeping  its 
right  ascension  equal  to  the 
mean  longitude  of  the  real 
sun.  For  some  purposes, 
as  in  dealing  with  the  tides, 
it  is  convenient  to  use  lunar 
time,  which  is  simply  the 
hour-angle  of  the  moon  at 
any  moment. 

423.  Twilight  is  caused 
by  the  reflection  of  sunlight 
from  the  upper  portions  of  the 
earth's  atmosphere.  After  the 
sun  has  set,  its  rays  still  con- 
tinue to  shine  through  the  air  above  the  observer's  head,  and  twilight 
continues  as  long  as  any  portion  of  this  illuminated  air  can  be  seen 
from  where  he  stands.  It  is  considered  to  end  when  stars  of  the 
sixth  magnitude  become  visible  near  the  zenith,  which  does  not  occur 
until  the  sun  is  about  18°  below  the  horizon ;  but  this  is  not  strictly 
the  same  for  all  places. 

The  duration  of  twilight  varies  with  the  season  and  with  the 
observer's  latitude.  In  latitude  40°  it  is  about  90  minutes  on  March 
1st  and  Oct.  12th;  but  more  than  two  hours  at  the  summer  solstice. 
In  latitudes  above  50°,  when  the  days  are  longest,  twilight  never  quite 
disappears,  even  at  midnight.  On  the  mountains  of  Peru,  on  the 
other  hand,  it  is  said  never  to  last  more  than  half  an  hour. 

424.  Methods  of  determining  Latitude  by  Other  Observa- 
tions than  those  of  Circumpolar  Stars  (supplementary  to  Art. 
81).  —  To  determine  the  latitude  by  observations  of  a  circum- 
polar  star,  the  observer  must  remain  at  the  same  station  at 
least  twelve  hours.  The  latitude  can  be  determined,  however, 
with  a  good  instrument,  with  almost  equal  precision,  by  ob- 
serving the  meridian  altitude,  or  zenith  distance,  of  a  body  whose 


§  424]  DETEKMINATION  OF  LATITUDE.  315 

declination  is  accurately  known.     In  Fig.  94  the  circle  AQPB 

is  the  meridian,  Q  and  P  being  respectively  the  equator  and 

the  pole,  and  Z  the  zenith.     QZ  is  evidently  the  declination 

of  the  zenith  (i.e.,  the  distance  of 

the    zenith    from    the    celestial 

equator)  and  is  equal  to  PB,  the 

latitude  of  the  observer,  or  height 

of  the  pole.     Suppose  now  that 

we   observe   Zs,  i.e.,  the   zenith 

distance  of  the  star  s,  south  of 

,1  •,-!  .,  ,-1  FIG.  94.  —  Determination  of  Latitude. 

the  zenith,  as  it  crosses  the  me- 
ridian, and  that  we  know  Qs,  the  declination  of  the  star. 
Evidently  QZ  =  Qs  +  sZ-,  i.e.,  the  latitude  equals  the  declina- 
tion of  the  star  plus  its  zenith  distance.  If  the  star  were  at  s', 
south  of  the  equator,  the  same  equation  would  hold  good 
algebraically,  because  the  declination,  Qs',  is  a  minus  quantity. 
If  the  star  were  at  n,  between  the  zenith  and  the  pole,  we 
should  have :  Latitude  equals  the  declination  of  the  star  minus 
the  zenith  distance.  This  is  the  method  actually  used  at  sea 
(Art.  426),  the  sun  being  the  object  observed. 

There  are  many  other  methods  in  use,  as,  for  instance,  that 
by  the  zenith  telescope  and  that  by  the  prime-vertical  instru- 
ment, which  are  practically  more  convenient  and  more  accurate 
than  either  of  the  two  described,  but  they  are  more  compli- 
cated, and  their  explanation  would  take  us  too  far.  The 
reader  is  referred  to  General  Astronomy,  Arts.  104-107. 

FINDING  THE  PLACE  OF  A  SHIP. 

425.  The  determination  of  the  place  of  a  ship  at  sea  is, 
from  the  economic  point  of  view,  the  most  important  problem 
of  Astronomy.  National  observatories  and  nautical  almanacs 
were  established,  and  are  maintained,  principally  to  supply  the 
mariner  with  the  data  needed  to  make  this  determination 
accurately  and  promptly.  The  methods  employed  are  neces- 


316  APPENDIX.  [§  425 

sarily  such  that  the  required  observations  can  be  made  with 
the  sextant  and  chronometer,  since  fixed  instruments,  like  the 
transit  instrument  and  meridian  circle,  are  obviously  out  of 
the  question  on  board  a  vessel. 

426.  Latitude  at  Sea.  —  This  is  obtained  by  observing  with 
the  sextant  the  sun's  maximum  altitude,  which  is  reached 
when  the  sun  is  crossing  the  meridian. 

Since  at  sea  the  sailor  seldom  knows  beforehand  the  precise 
time  which  will  be  shown  by  his  chronometer  at  noon,  he 
takes  care  not  to  be  too  late,  and  begins  to  measure  the  sun's 
altitude  a  little  before  noon,  repeating  his  observations  every 
minute  or  two.  At  first  the  altitude  will  keep  increasing,  but 
when  noon  comes  the  sun  will  cease  rising,  and  then  begin  to 
descend.  The  observer  uses,  therefore,  the  maximum  altitude 
obtained,  which,  with  due  allowance  for  refraction  and  some 
other  corrections  (for  details,  see  larger  works)  gives  him  the 
true  altitude  of  the  sun's  centre.  Taking  this  from  90°,  we 
get  its  zenith  distance. 

Eef erring  now  to  Fig.  94,  in  which  the  circle  AQZPB  is 
the  meridian,  P  the  pole,  Z  the  zenith,  and  OQ  the  celestial 
equator  seen  edgewise,  we  see  that  PB,  the  altitude  of  the 
pole,  is  necessarily  equal  to  ZQ,  the  distance  from  the  zenith 
to  the  equator.  Now  from  the  almanac  we  find  the  declina- 
tion of  the  sun,  Qs,  for  the  day  on  which  the  observations  are 
made.1  We  have  only  to  add  to  this,  Zs,  the  measured  dis- 
tance of  the  sun  from  the  zenith,  to  obtain  QZ,  which  is  the 
observer's  latitude. 

It  is  easy  in  this  way,  with  a  good  sextant,  to  get  the  lati- 
tude within  about  half  a  minute  of  arc,  or,  roughly,  about 
half  a  mile,  which  is  quite  sufficiently  accurate  for  nautical 
purposes. 

1  If  the  sun  happened  to  be  south  of  the  equator  (in  the  winter),  as  at 
s',  we  should  have  ZQ  equals  Zs  —s'Q. 


§  427]  LOCAL   TIME   AND   LONGITUDE   AT   SEA.  317 

427.  Determination  of  Local  Time  and  Longitude  at  Sea. 

—  The  usual  method  now  employed  for  the  longitude  depends 
upon  the  chronometer.  This  is  carefully  'rated'  in  port; 
i.e.,  its  error  and  its  daily  gain  or  loss  are  determined  by  com- 
parisons with  an  accurate  clock  for  a  week  or  two,  the  clock 
itself  being  kept  correct  to  Greenwich  time  by  transit  obser- 
vations. By  merely  allowing  for  the  gain  or  loss  since  leaving 
port,  and  adding  this  gain  or  loss  to  the  ' error'  (Art.  417), 
which  the  chronometer  had  when  brought  on  board,  the  sea- 
man at  once  obtains  the  error  of  the  chronometer  on  Green- 
wich time  at  any  moment ;  and  allowing  for  this  error,  he  has 
the  Greenwich  time  itself,  with  an  accuracy  which  depends 
only  pn  the  constancy  of  the  chronometer's  rate :  it  makes  no 
difference  whether  it  is  gaining  much  or  little,  provided  its 
daily  rate  is  steady. 

He  must  also  determine  his  own  local  time;  and  this  must 
be  done  with  the  sextant,  since,  as  was  said  before,  an  instru- 
ment like  the  transit  cannot  be  used  at  sea.  He  does  it  by 
measuring  the  altitude  of  the  sun,  not  at  or  near  noon,  as  often 
supposed,  but  when  the  sun  is  as  near  due  east  or  west  as  cir- 
cumstances permit.  From  such  an  observation  the  sun's  hour- 
angle,  i.e.,  the  apparent  solar  time  (Art.  422),  is  easily  found, 
by  a  trigonometrical  calculation,  provided  the  ship's  latitude 
is  known.  (For  the  method  of  calculation,  see  General  As- 
tronomy, Art.  116.) 

The  longitude  follows  at  once,  being  simply  the  difference 
between  the  Greenwich  time  and  the  local  time. 

In  certain  cases  where  the  chronometers  have  been  for 
some  reason  disturbed,  the  mariner  is  obliged  to  get  his  Green- 
wich time  by  observing  with  a  sextant  the  distance  of  the 
moon  from  some  neighboring  fixed  star,  but  the  results  thus 
obtained  are  comparatively  inaccurate  and  unsatisfactory. 

428.  To  find  the  Form  of  the  Earth's  Orbit  (supplementary 
to  Art.  119).  —  Take  the  point  S  (Fig.  95)  for  the  sun,  and 


318 


APPENDIX. 


[§428 


draw  from  it  a  line,  SO,  directed  toward  the  vernal  equinox, 
from  which  longitudes  are  measured.  Lay  off  from  S  lines 
indefinite  in  length,  making  angles  with  80  equal  to  the 

earth's  longitude  as  seen 
from  the  sun  on  each 
of  the  days  when  the 
observations  are  made 
(earth's  longitude  equals 
sun's  longitude  +  180°). 
We  shall  thus  get  a  sort 
of  "spider,"  showing  the 
direction  of  the  earth  as 
seen  from  the  sun  on 
each  of  those  days. 

10  /        11  /  Next,  as  to  the   dis- 

tances. While  the  ap- 
parent diameter  of  the 
sun  does  not  tell  us  its 

absolute  distance  from  the  earth,  unless  we  know  his  diameter 
in  miles,  yet  the  changes  in  the  apparent  diameter  do  inform 
us  as  to  the  relative  distance  at  different  times,  since  the  nearer 
we  are  to  the  sun,  the  larger  it  looks.  If,  then,  on  the  legs  of 
the  "  spider  "  we  lay  off  distances  inversely  proportional  to  the 
number  of  seconds  of  arc  in  the  sun's  measured  diameter  at 
each  date,  these  distances  will  be  proportional  to  the  true  dis- 
tance of  the  earth  from  the  sun,  and  the  curve  joining  the 
points  thus  obtained  will  be  a  true  map  of  the  earth's  orbit, 
though  without  any  scale  of  miles.  When  the  operation  is 
performed,  we  find  that  the  orbit  is  an  ellipse  of  small  eccen- 
tricity, with  the  sun  not  at  the  centre,  but  in  one  of  the  two 
foci. 


FIG.  95. 
Determination  of  the  Form  of  the  Earth's  Orbit. 


429.  The  Ellipse,  and  Definitions  relating  to  it  (supplemen- 
tary to  Arts.  119,  120).  —  If  we  drive  two  pins  into  a  board,  as 
at  F  and  S  in  Fig.  96,  and  put  a  looped  thread  around  the 


§429] 


DEFINITIONS   RELATING  TO   THE  ELLIPSE. 


319 


pins,  attached  to  the  point  of  a  pencil,  P,  then  on  carrying 

the  pencil  around  it  will  mark  out  an  ellipse.     The  pins,  F 

and  S,  are  the  "  foci "  of  the 

ellipse,  and   C  is  its  centre. 

From   the   manner   in   which 

the  ellipse  is  constructed, .  it 

is  clear  that  at  any  point,  P, 

on  its  outline,  the  sum  of  the 

two   lines,  PS  and  PF,  will 

always  be  the  same,  and  equal 

to  the  line  AA'.     The  length 

of  the  ellipse,  AA',  is  called  FlG"  96- The  Ellip8e' 

its  major  axis,  and  AC  its  semi-major  axis,  which  is  usually 

designated  by  a,  while  the  semi-minor  axis,  BC,  is  lettered  &. 

CS 
The  fraction,  — -,  is  called  the  eccentricity  of  the  ellipse,  and 

AC 

determines  the  shape  of  the  oval.  Its  usual  symbol  is  e.  If  e 
is  nearly  unity,  —  i.e.t  if  CS  is  nearly  equal  to  CA, — the  oval 
will  be  very  narrow  compared  with  its  length ;  but  if  CS  is 
very  small  compared  with  CA,  the  ellipse  will  be  almost  round. 
Taken  together,  a  and  e  determine  the  size  and  form  of  the 
oval.  The  ellipse  is  called  a  '  conic/  because  when  a  cone  is 
cut  across  obliquely  the  section  is  elliptical  (see  Art.  440). 

430.  Problems  illustrating  the  « Harmonic  Law '  (supple- 
mentary to  Art.  220).  —  To  aid  the  student  in  apprehending  the 
meaning  and  scope  of  Kepler's  third  law,  we  give  a  few  simple  exam- 
ples of  its  application. 

1.  What  would  be  the  period  of  a  planet  having  a  mean  distance 
from  the  sun  of  one  hundred  astronomical  units ;  i.e.,  a  distance  a 
hundred  times  that  of  the  earth  ? 

P:1003=l2(year):X2; 
whence,  X  (in  years)  =  VlOO8  =  1000  years. 

2.  What  would  be  the  distance  from  the  sun  of  a  planet  having  a 
period  of  125  years  ? 

I2  (year)  :  1252  =  1«  :  Z8;  whence  X  =  v/1252  =  25  astron.  units. 


320  APPENDIX.  [§  430 

3.  What  would  be  the  period  of  a  satellite  revolving  close  to  the 
earth's  surface  ? 

(Moon's  Dist.)8  :  (Dist.  of  Satellite)8=  (27.3  days)2:  X\ 
or,  608  :  I8  =  27.32  :  X2 ; 

whence,  X  =  27j2  days  -  1"  24m. 

V608 

4.  How  much  would  an  increase  of  10  per  cent  in  the  earth's  dis- 
tance from  the  sun  lengthen  the  year? 


1008  :  HO8  =  (365})2  :  X*,  whence  Z2  =  X 


X  being  the  new  length  of  the  year.     X  is  found  by  logarithmic  com- 
putation to  be  421.38  days.     The  increase  is  56.13  days. 

5.  What  is  the  distance  from  the  sun  of  an  asteroid  with  a  period 
of  3£  years  ? 

I2  (year):  3.52  =  1«  :  Dist.3 

.-.  Dist.  =  \/(3^T2  =  v/12^5  =  2.305  astron.  units. 

431.  The  Equation  of  Light.  —  When  we  observe  a  celestial 
body,  we  see  it  not  as  it  is  at  the  moment  of  observation,  but 
as  it  was  at  the  moment  when  the  light  which  we  see  left  it. 
If  we  know  its  distance  in  astronomical  units,  and  know  how 
long  light  takes  to  traverse  that  unit,  we  can  at  once  correct 
our  observation  by  simply  dating  it  back  to  the  time  when  the 
light  started  from  the  object.  The  necessary  correction  is 
called  the  "  equation  of  light,"  and  the  time  required  by  light  to 
traverse  the  astronomical  unit  of  distance  is  called  the  "Con- 
stant of  the  Light-equation"  (not  quite  500  seconds,  as 
we  shall  see). 

It  was  in  1675  that  Roemer,  the  Danish  astronomer  (the  inventor 
of  the  transit  instrument,  meridian-circle,  and  prime-vertical  instru- 
ment, —  a  man  almost  a  century  in  advance  of  his  day),  found  that 
the  eclipses  of  Jupiter's  satellites  show  a  peculiar  variation  in  their 
times  of  occurrence,  which  he  explained  as  due  to  the  time  taken  by 
light  to  pass  through  space.  His  bold  and  original  suggestion  was 


§  431] 


THE  EQUATION   OF   LIGHT. 


321 


neglected  for  more  than  fifty  years,  until  long  after  his  death,  when 
Bradley 's  discovery  of  aberration  (Art.  435)  proved  the  correctness  of 
his  views. 


432.  Determination  of  the  Constant  of  the  Equation  of 
Light.  —  Eclipses  of  the  satellites  of  Jupiter  recur  at  intervals 
which  are  really  almost  exactly  equal  (the  perturbations  being 
very  slight),  and  the  interval  can  easily  be  determined  and  the 
times  tabulated.  But  if  we  thus  predict  the  times  of  the 
eclipses  during  a  whole  synodic  period  of  the  planet,  then,  be- 
ginning at  the  time  of  opposition,  it  is  found  that  as  the  planet 
recedes  from  the  earth,  the  eclipses,  as  observed,  fall  constantly 
more  and  more  behindhand,  and  by  precisely,  the  same  amount 
for  all  four  satellites.  The 
difference  between  the  pre- 
dicted and  observed  time 
continues  to  increase  until 
the  planet  is  near  conjunc- 
tion, when  the  eclipses  are 
about  16m  38s  later  than  the 
prediction.  After  the  con- 
junction they  quicken  their 
pace,  and  make  up  the  loss, 
so  that  when  opposition  is 
reached  once  more  they  are 
again  on  time. 

It  is  easy  to  see  from 
Fig.  97  that  at  opposition 
the  planet  is  nearer  the  earth  than  at  conjunction  by  just  two 
astronomical  units.  At  opposition  the  distance  between  Jupi- 
ter and  the  earth  is  JA,  while  six  and  a  half  months  later,, 
at  the  time  of  Jupiter's  superior  conjunction,  it  is  JB.  The 
difference  between  JA  and  JB  is  just  twice  the  distance  from 
8  to  A. 

The  whole  apparent  retardation  of  eclipses  between  opposi- 


FIG.  97.  — The  Equation  of  Light. 


322  APPENDIX.  [§  432 

tion  and  conjunction  must  therefore  be  exactly  twice  the  time 1 
required  for  light  to  come  from  the  sun  to  the  earth.  In  this  way 
the  "  light-equation  constant "  is  found  to  be  very  nearly  499 
seconds,  or  8  minutes  19  seconds,  with  a  probable  error  of 
perhaps  two  seconds. 

433.  Since  these  eclipses  are  gradual  phenomena,  the  determination 
of  the  exact  moment  of  a  satellite's  disappearance  or  reappearance  is 
very  difficult,  and  this  renders  the  result  somewhat  uncertain.    Prof.  E. 
C.  Pickering  of  Cambridge  has  proposed  to  utilize  photometric  observa- 
tions for  the  purpose  of  making  the  determination  more  precise,  and 
two  series  of  observations  of  this  sort,  and  for  this  purpose,  are  now 
in  progress,  —  one  in  Cambridge,   United  States,  and  the  other  at 
Paris  under  the  direction  of  Cornu,  who  has  devised  a  similar  plan. 
Pickering  has  also » applied  photography  to  the  observation  of  these 
eclipses  with  encouraging  success. 

434.  The  Distance  of  the  Sun  determined  by  the  "Light- 
equation."  —  Until  1849  our  only  knowledge  of  the  velocity  of 
light  was  obtained  from  such  observations  of  Jupiter's  satel- 
lites.    By  assuming  as  known  the  earth's  distance  from  the  sun, 
the  velocity  of  light  can  be  obtained  when  we  know  the  time 
occupied  by  light  in  coming  from  the  sun. 

At  present,  however,  the  case  is  reversed.  We  can  deter- 
mine the  velocity  of  light  by  two  independent  experimental 
methods,  and  with  a  surprising  degree  of  accuracy.  Then, 
knowing  this  velocity  and  the  "light-equation  constant,"  we 
can  deduce  the  distance  of  the  sun.  According  to  the  latest 
determinations  the  velocity  of  light  is  186,330  miles  per  second. 
Multiplying  this  by  499  we  get  92,979,000  miles  for  the  sun's 
distance  (compare  Art.  436). 

1  The  student's  attention  is  specially  directed  to  the  point  that  the  ob- 
servations of  the  eclipses  of  Jupiter's  satellites  give  directly  neither  the 
velocity  of  light  nor  the  distance  of  the  sun :  they  give  only  the  time  re- 
quired by  light  to  make  the  journey  from  the  sun.  Many  elementary 
text-books,  especially  the  older  ones,  state  the  case  carelessly. 


435] 


ABERRATION   OF   LIGHT. 


323 


435.  Aberration  of  Light.  —  The  fact  that  light  is  not  trans- 
mitted instantaneously  causes  the  apparent  displacement  of 
an  object  viewed  from  any  moving  station,  unless  the  motion 
is  directly  towards  or  from  that  object.  If  the  motion  of 
the  observer  is  not  rapid,  this  displacement,  or  "aberration," 
is  insensible ;  but  the  earth  moves  so  swiftly  (18J  miles 
per  second)  that  it  is  easily  observable  in  the  case  of  the 
stars.  Astronomical  aberration  may  be  defined,  therefore,  as 
the  apparent  displacement  of  a  heavenly  body  due  to  the  combina- 
tion of  the  orbital  motion  of  the  earth  with  that  of  light  —  the 
direction  in  which  we  have  to  point  our  telescope  in  observing 
a  star  is  not  the  same  as  if  the  earth  were  at  rest. 

We  may  illustrate  this  by  considering  what  would  happen  in  the 
case  of  falling  rain-drops.  Suppose  the  observer  standing  with  a  tube 
in  his  hand  while  the  drops 
are  falling  straight  down:  if 
he  wishes  to  have  the  drops 
descend  through  the  middle  of 
the  tube  without  touching  the 
sides,  he  must  keep  it  vertical 
so  long  as  he  stands  still ;  but 
if  he  advances  in  any  direction 
the  drops  will  strike  the  side  of 
the  tube,  and  he  must  thrust 
forward  its  upper  end  (Fig.  98) 
by  an  amount  which  equals 


m 


u 


FIG.  98. —Aberration. 


the  advance  he  makes  while  a 

drop  is  falling  through  it ;  i.e., 

he  must  incline  the  tube  forward  at  an  angle,  depending  both  upon 

the  velocity  of  the  rain-drop  and  the  swiftness  of  his  own  motion, 

so  that  when  the  drop,  which  entered  the  tube  at  B,  reaches  A',  the 

bottom  of  the  tube  will  be  there  also. 

It  is  true  that  this  illustration  is  not  a  demonstration,  because  light 
does  not  consist  of  particles  coming  towards  us,  but  of  waves  trans- 
mitted through  the  ether  of  space.  But  it  has  been  shown  (though 
the  proof  is  by  no  means  elementary)  that  within  very  narrow  limits, 
the  apparent  direction  of  a  wave  is  affected  in  precisely  the  same  way 
as  that  of  a  moving  projectile. 


324  APPENDIX.  [§  435 

The  best  observations  show  that  a  star  situated  on  a  line  at 
right  angles  to  the  direction  of  the  earth's  motion,  is  thus 
apparently  displaced  by  an  angle  of  about  20".5.  The  latest 
and  most  trustworthy  determination  by  Nyren  of  Pulkowa 
makes  it  20".492. 

This  is  the  so-called  "  CONSTANT  OF  ABERRATION/' 
If  the  star  is  in  a  different  part  of  the  sky,  its  displacement 
will  be  less,  the  amount  being  easily  calculated  when  the  star's 
position  is  given. 

436.  Determination  of  the  Sun's  Distance  by  Means  of  the 
Aberration  of  Light.  —  The  constant  of  aberration,  a,  and 
the  two  velocities,  that  of  the  earth  in  its  orbit,  u,  and  the 
velocity  of  light,  V,  are  connected  by  the  very  simple  equation 

a  =  206265  x      ;  whence  «  =  x  V. 


When,  therefore,  we  have  ascertained  the  value  of  a  (20".  492) 
from  observations  of  the  stars,  and  of  V  (186,330  miles,  ac- 
cording to  the  most  recent  determinations  by  Michelson  and 
Newcomb)  by  physical  experiments,  we  can  immediately  find 
u,  the  velocity  of  the  earth  in  her  orbit.  The  circumference  of 
the  earth's  orbit  is  then  found  by  multiplying  this  velocity,  w, 
by  the  number  of  seconds  in  a  sidereal  year  (Art.  127)  ;  and 
from  this  we  get  the  radius  of  the  orbit,  or  the  earth's  mean  dis- 
tance from  the  sun,  by  dividing  the  circumference  by  2?r  (?r  = 
3.14159).  Using  the  values  above  given,  the  mean  distance  of 
the  sun  comes  out  92,975500  miles. 

But  the  uncertainty  of  a  is  probably  as  much  as  0".03,  and 
this  affects  the  distance  proportionally,  say  one  part  in  600,  or 
150,000  miles.  Still,  the  method  is  one  of  the  very  best  of 
all  that  we  possess  for  determining  in  miles  the  value  of  "  the 
Astronomical  Unit." 

437.  De  1'Isle's  Method  of  determining  the  Sun's  Parallax 
by  a  Transit  of  Venus.  —  We  have  thus  (Arts.  434  and  436) 


§  437]  DETERMINING  THE   SUN'S   PARALLAX.  325 

two  methods  by  which  the  mean  distance  of  the  sun  from  the 
earth  can  be  determined.  They  both  depend  upon  a  knowl- 
edge of  the  velocity  of  light,  and  of  course  were  unavailable 
before  1849,  when  Fizeau  first  succeeded  in  actually  measuring 
it.  Before  that  time  it  was  necessary  to  rely  entirely  upon 
observations  of  either  Mars  or  Venus,  made  at  times  when 
they  come  specially  near  us. 

Most  of  the  methods  of  getting  the  sun's  parallax  and  dis- 
tance from  such  observations  depend  upon  our  having  a  pre- 
vious knowledge  of  the  relative  distances  of  the  planets  from 
the  sun.  These  relative  distances  were  ascertained  centuries 
ago.  Copernicus  knew  them  nearly  as  accurately  as  we  have 
them  now;  but  since  we  have  not  explained  in  this  book  how 


E 

FIG.  99.  —  Transit  of  Venue. 

they  are  found  (the  explanation  involves  a  little  Trigonom- 
etry), we  limit  ourselves  to  giving  here  a  single  very  simple 
method,  which  requires  a  previous  knowledge  not  of  the  rela- 
tive distances  of  Venus  and  the  earth  from  the  sun,  but  only 
of  the  synodic  period  of  the  planet  (Art.  228) ;  i.e.,  the  time  in 
which  she  gains  one  entire  revolution  upon  the  earth.  This 
is  584  days,  as  has  been  known  from  remote  antiquity. 

Fig.  99  represents  things  at  a  transit  of  Venus,  as  they  would 
be  seen  by  one  looking  down  from  an  infinitely  distant  point 
above  the  earth's  north  pole.  As  seen  from  the  earth  itself, 
Venus  would  appear  to  cross  the  sun,  striking  the  disc  on 
the  east  side  and  moving  straight  across  to  the  west,  mak- 
ing four  '  contacts '  with  the  edge  of  the  sun  as  shown  in 
Fig.  100. 


326  APPENDIX.  [§  438 

438.  Suppose,  now,  that  two  observers,  E  and  W  (Fig.  99), 
are  stationed  opposite  each,  other,  and  near  the  earth's  equator. 

E  will  see  Venus  strike  the  sun's 
disc  before  W  does,  and  if  they 
both  observe  the  moment  of  con- 
tact, in  Greenwich  time,  the  differ- 
ence between  their  records  will  be 
the  time  it  takes  Venus  to  move 
over  the  arc  from  V\  to  F2.  From 
the  figure  it  is  clear  that  the  angle, 
ViDVz,  is  the  same  as  EDW,  the 
,.  100.  earth's  apparent  diameter  seen  from 

Contacts  in  a  Transit  of  Venus.        tJte  SUU}  an(J  this   is    at   Once   known 

when  we  have  the  time  from  Vi  to  F2. 

Since  Venus  gains  one  revolution  in  584  days,  in  one  day 
she  will  gain  -^^  of  a  revolution,  or  37'  (very  nearly),  and 
this  will  make  her  gain  1".54  in  one  minute.  Now  it  is  found 
that  the  difference  between  the  moments  of  contact  at  two 
stations  situated  like  E  and  W  is  about  llm  25s,  and  hence  that 
the  diameter  of  the  earth  as  seen  from  the  sun  is  17".6,  or  the 
sun's  horizontal  parallax  (Art.  139)  is  8".8 ;  from  which  its 
distance  is  easily  found  (Art.  140). 

The  reader  will  see  that  the  two  observers  must  know  their 
longitudes  accurately,  in  order  to  be  sure  of  the  correct  Green- 
wich time.  Moreover,  the  two  stations  can  never  be  quite 
exactly  opposite  each  other,  but  stations  a  little  nearer  together 
must  be  taken  and  proper  allowances  made.  Finally,  we  are 
very  sorry  to  add  that  the  necessary  observations  of  the  mo- 
ment when  Venus  reaches  the  edge  of  the  sun's  disc  cannot  be 
made  with  the  accuracy  which  is  desirable,  owing  to  the  effect 
of  the  planet's  atmosphere  (see  Art.  248) ;  so  that  practically 
the  method  is  less  accurate  than  might  be  hoped.  For  fur- 
ther details,  see  General  Astronomy,  Chapter  XVI. 

439.  The  Parabola   (supplementary  to   Arts.  292-298). — This 
differs  from  the  ellipse  in  never   coming  around  into  itself. 


§439] 


THE  PAEABOLA. 


327 


In  Fig.  101,  the  curves  PAl}  PA2  and  PA3,  are  ellipses  of  dif- 
ferent length,  all  having  S  at  one  of  their  foci.  The  first  and 
smallest  of  the  ellipses  is  nearly  circular,  and  shaped  about 
like  the  orbit  of  Mercury ;  the  next,  more  eccentric  than  the 
orbit  of  any  asteroid ;  and  the  third  still  more  so.  Now  if  we 


FIG.  101.  — Ellipse,  Parabola,  and  Hyperbola. 

imagine  the  point  F  carried  farther  and  farther  to  the  right, 
the  ellipse  will  grow  larger  and  longer,  until  when  F  is  infi- 
nitely far  away  the  curve  will  become  a  parabola. 

Of  course  if  the  point  F  is  very  distant,  even  if  not  infinitely 
so,  the  part  of  the  curve  near  S  will  agree  with  the  parabola 
so  closely  that  no  one  could  distinguish  between  them. 

All  ellipses  that  have  S  for  the  focus  and  P  for  the  perihe- 
lion lie  inside  of  the  parabola,  while  another  set  of  conic  curves 
called  hyperbolas,  with  the  same  focus  and  perihelion,  lie  en- 
tirely outside  of  it,  which  is,  so  to  speak,  a  sort  of  boundary 
or  division  line  between  the  ellipses  and  hyperbolas  which 
have  this  focus  and  perihelion. 


328 


APPENDIX. 


[§440 


440.  The  Conic  Sections.  —  The  way  in  which  these  curves, 
—  the  ellipse,  parabola,  and  hyperbola  —  are  formed  by  sec- 
tions of  the  cone  is  shown  by  Fig.  102. 

(a)  If  the  cone  be  cut  by  a 
plane  which   makes   with  its 
axis,  VC,  an  angle  greater  than 
BVC,  the  plane  of  the  section 
will  cut  completely  across  the 
cone,  and  the  section  EF  will 
be  an  ellipse,  which  will  vary 
in  shape  and  size  according  to 
the  position  of  the  plane.  The 
circle  is  simply  a  special  case 
when  the  cutting  plane  is  per- 
pendicular to  the  axis,  as  NM. 

(b)  When  the  cutting  plane 
makes  with  the  axis  an  angle 
less  than  B  VC  (the  semi-angle 
of  the  cone),  it  plunges  contin- 
ually deeper  and  deeper  into 
the  cone  and  never  comes  out 
on  the  other  side  (the  cone  is 
supposed    to    be    indefinitely 
prolonged).      The    section   in 
this  case  is  an  hyperbola,  GHK. 
If  the  plane  of  the  section  be 
produced  upward,  however,  it 
encounters    the    "cone  pro- 
duced,"   cutting   out   from  it 
a  second    hyperbola,  G'H'K', 
precisely  like  the  original  one, 

but  turned  in  the  opposite  direction. 

The  axis  of  the  hyperbola  is  always  reckoned  as  negative, 
lying  outside  of  the  curve  itself :  in  the  figure,  it  is  the  line 
HH'.  The  centre  of  the  hyperbola  is  the  middle  point  of  this 
axis,  a  point  also  outside  of  the  curve. 


FIG.  102. —The  Conies. 


§440]  STELLAK  PARALLAX.  329 

(c)  When  the  angle  made  by  the  cutting  plane  with  the 
axis  is  exactly  equal  to  the  cone's  semi-angle,  the  plane  will 
be  parallel  to  the  side  of  the  cone,  and  we  then  get  the  special 
case  of  the  parabola,  RPO,  which  forms  a  partition,  so  to 
speak,  between  the  infinite  variety  of  ellipses  and  hyperbolas 
which  can  be  cut  from  a  given  cone.  All  parabolas  are  of  the 
same  shape,  just  as  all  circles  are,  differing  only  in  size.  The 
fact  is  by  no  means  self-evident,  and  we  cannot  stop  to  prove 
it,  but  it  is  true. 

441.  Determination  of  the  Parallax  of  a  Star  (supplemen- 
tary to  Art.  343).  —  The  determination  of  the  parallax  of  stars 
had  been   attempted  over  and  over  again  from  the  time  of 
Tycho  Brahe  down,  but  without  success  until,  in  1838,  Bessel 
at  last  demonstrated  and  measured  the  parallax  of  61  Cygni ; 
and  the  next  year  Henderson,  of   the  Cape  of   Good  Hope, 
determined  that  of  Alpha  Centauri.    The  operation  of  measur- 
ing the  parallax  of  a  star  is  on  the  whole  the  most  delicate 
in  the  whole  range  of  practical  Astronomy.     Two   methods 
have  been  used  so  far,  known  as  the  absolute  and  the  differential. 

442.  The  Absolute  Method  consists  in  making  the  most  scru- 
pulously precise   observations  of  the   star's   right  ascension 
and  declination  with  the  meridian  circle  at  different  times 
through  the  course  of  an   entire   year,  applying   rigidly  all 
known  corrections  (for  precession,  aberration,  proper  motion, 
etc.),  and  then  examining  the  deduced  positions.     If  the  star 
is  without  parallax,  these  positions  will  all  agree.     If  the  star 
has  a  sensible  parallax,  they  will  show,  on  the  other  hand, 
when  plotted  on  a  chart,  an  apparent  annual  orbital  motion  of 
the  star  in  a  little  ellipse,  the  major  axis  of  which  is  twice  the 
star's  annual  parallax,  as  can  easily  be  shown. 

Theoretically,  the  method  is  perfect ;  practically,  it  seldom 
gives  satisfactory  results,  because  the  annual  changes  of  tem- 
perature and  moisture  disturb  the  instrument  in  such  a  way 


330  APPENDIX.  [§  44«i 

that  the  instrumental  errors  intertwine  themselves  with  the 
parallax  of  a  star  in  a  manner  that  defies  disentanglement. 
No  process  of  multiplying  observations  and  taking  averages 
helps  the  matter  very  much,  because  the  instrumental  errors 
are  themselves  periodic  annually,  just  as  is  the  parallax ; 
still,  in  a  few  cases  the  method  has  proved  successful,  as  in 
the  case  of  Alpha  Centauri,  above  cited. 

443.  The  Differential  Method.  —  This,   the  method  which 
has  principally  proved  successful  thus  far,  consists  in  meas- 
uring the  annual  displacement  of  the  star  whose  parallax  we 
are  seeking,  with  respect  to  other  small  stars  near  it  in  appar- 
ent position  (i.e.,  within  a  few  minutes  of  arc),  but  presuma- 
bly so  far  beyond  as  to  have  no  sensible  parallax  of  their  own. 

If,  for  instance,  the  observer  notes  the  apparent  place  of  an 
object  at  no  great  distance  from  him  with  reference  to  the 
trees  on  a  distant  hill-side,  and  then  moves  a  few  feet  one  way 
or  the  other,  he  will  see  that  the  nearer  object  shifts  its  posi- 
tion with  reference  to  the  trees.  In  the  same  way,  on  account 
of  the  earth's  orbital  motion,  those  stars  which  are  very  near 
the  earth  appear  every  year  to  shift  slightly  backwards  and 
forwards  with  respect  to  those  that  are  far  beyond  them ;  and 
by  measuring  the  amount  of  this  shift  it  is  possible  to  deduce 
approximately  the  parallax  and  distance  of  the  nearer  stars. 

We  say  approximately,  because  the  shift  thus  measured  is 
not  really  the  whole  parallax  of  the  nearer  star,  but  only 
the  difference  between  that  parallax  and  the  parallax  of  the 
remote  objects  with  which  it  is  compared;  so  that  observa- 
tions, if  accurately  made,  will  always  give  us  for  the  nearer 
star  a  parallax  too  small,  if  anything,  —  never  too  large ;  and, 
as  a  consequence,  the  distance  of  the  nearer  star  determined 
in  this  way  will  come  out  a  little  too  large,  and  never  too  small. 

444.  The  necessary  measurements,  if  the  comparison  stars 
are  within  a  minute  or  two  of  arc,  may  be  made  with  the  wire 


§  444]  THE  SLITLESS   SPECTROSCOPE.  331 

micrometer  (Art.  415) ;  but  if  the  distance  exceeds  a  few  min- 
utes, we  must  resort  to  the  "  heliometer  "  (see  General  Astron- 
omy, Art.  677),  with  which  Bessel  first  succeeded ;  or  we  may 
employ  photography,  which  Professor  Pritchard  at  Oxford 
has  recently  been  doing  with  remarkable  success. 

On  the  whole,  the  differential  method,  notwithstanding  the 
fundamental  objection  to  it,  that  it  never  gives  us  the  entire 
parallax  of  the  star,  is  at  present  more  trustworthy  than  the 
other. 

It  is  obviously  necessary  to  choose  for  observation  by  either 
method  those  stars  that  are  presumably  near  us.  The  most 
important  indication  of  nearness  in  a  star  is  a  large  proper 
motion ;  brightness,  also,  is  of  course  confirmatory.  Still, 
neither  of  these  indications  is  certain.  A  star  which  happens 
to  be  moving  directly  towards  or  from  us  shows  no  proper 
motion  at  all,  however  near  it  may  be ;  and  the  faint  stars  are 
so  very  much  more  numerous  than  the  brighter  ones  that 
among  their  millions  it  is  quite  likely  that  we  shall  ultimately 
find  individuals  which  are  even  nearer  than  Alpha  Centauri. 

445,  (Supplementary  to  Art.  364.)  —  The  slitless  spectroscope 
has  three  great  advantages :  (1)  it  saves  all  the  light  which 
comes  from  the  star,  much  of  which  in  the  usual  form  of  the 
instrument  is  lost  in  the  jaws  of  the  slit ;  (2)  by  taking  advan- 
tage of  the  length  of  a  large  telescope,  it  produces  a  long  spec- 
trum with  even  a  single  prism ;  (3)  and  most  important  of  all, 
it  gives  on  the  same  plate,  and  with  a  single  exposure,  the 
spectra  of  all  the  many  stars  (sometimes  more  than  a  hun- 
dred) whose  images  fall  upon  the  plate. 

On  the  other  hand,  the  giving  up  of  the  slit  precludes  the 
usual  methods  of  identifying  the  lines  and  measuring  their 
displacements,  by  actually  confronting  them  with  comparison 
spectra.  For  instance,  it  has  not  yet  been  found  possible  to 
use  the  slitless  spectroscope  for  determining  the  absolute 
motions  of  the  stars  in  the  line  of  sight. 


332  APPENDIX. 


SUGGESTIVE  QUESTIONS 


FOR    USE    IN    REVIEWS. 


To  many  of  these  questions  direct  answers  will  not  be 
found  in  the  book ;  but  the  principles  upon  which  the  answers 
depend  have  been  given,  and  the  student  will  have  to  use  his 
own  thinking  in  order  to  make  the  proper  application. 

1.  What  point  in  the  celestial  sphere  has  both  its  right  ascension 
and  declination  zero  ? 

2.  What  angle  does  the  (celestial)  equator  make  with  the  horizon 
at  this  place  ? 

3.  Name  the  (fourteen)  principal  points  in  the  celestial  sphere 
(zenith,  etc.). 

4.  What  important  circles  in  the  heavens  have  no  correlatives  on 
the  surface  of  the  earth  ? 

5.  What  constellation  of  the  zodiac  rises  at  sunset  to-day,  and 
which  one  is  then  on  the  meridian  ?     (Use  the  star-maps.) 

6.  If  Vega  comes  to  the  meridian  at  8  o'clock  to-night,  at  what 
time  (approximately)  will  it  transit  eight  days  hence? 

7.  What  bright  star  can  I  observe  on  the  meridian  between  3  and 
4  P.M.,  in  the  middle  of  August?     (See  star-maps.) 

8.  Would  twilight  be  longer  or  shorter  at  the  summit  of  the  Peak 
of  Teneriffe  than  at  its  base  ?    Why  ? 

9.  The  declination  of  Vega  is  38°  41' ;  does  it  pass  the  meridian 
north  of  your  zenith,  or  south  of  it? 

10.  What  are  the  right  ascension  and  declination  of  the  north  pole 
of  the  ecliptic  ? 

11.  What  are  the  longitude  and  latitude  (celestial)  of  the  north 
celestial  pole  (the  one  near  the  Pole-star)  ? 


SUGGESTIVE  QUESTIONS.  333 

12.  Can  the  sun  ever  be  directly  overhead  where  you  live  ?    If  not, 
why  not  ? 

13.  What  is  the  zenith  distance  of  the  sun  at  noon  on  June  22d  in 
New  York  City  (lat.  40°  42')  ? 

14.  What  are  the  greatest  and  least  angles  made  by  the  ecliptic 
with  the  horizon  at  New  York  ?     Why  does  the  angle  vary  ? 

15.  If  the  obliquity  of  the  ecliptic  were  30°,  how  wide  would  the 
temperate  zone  be?    How  wide  if  the  obliquity  were  50°?    What 
must  the  obliquity  be  to  make  the  two  temperate  zones  each  as  wide 
as  the  torrid  zone  V 

16.  Does  the  equinox  always  occur  on  the  same  days  of  March  and 
September  ?    If  not,  why  not ;  and  how  much  c*an  the  date  vary  ? 

17.  Was  the  sun's  declination  at  noon  on  March  10th,  1887,  pre- 
cisely the  same  as  on  the  same  date  in  1889  ? 

18.  In  what  season  of  the  year  is  New  Year's  Day  in  Chili? 

19.  When  the  sun  is  in  the  constellation  Taurus,  in  what  sign  of 
the  zodiac  is  he  ? 

20.  In  what  constellation  is  the  sun  when  he  is  vertically  over  the 
tropic  of  Cancer ?     Near  what  star?     (See  star-map.) 

21.  When  are  day  and  night  most  unequal? 

22.  In  what  part  of  the  earth  are  the  days  longest  on  March  20th  ? 
On  June  20th  ?     On  Dec.  20th  ? 

23.  Why  is  it  warmest  in  the  United  States  when  the  earth  is 
farthest  from  the  sun? 

24.  What  will  be  the  Russian   date  corresponding  to  Feb.  28th, 
1900,  of  our  calendar  ?    To  May  28th  ? 

25.  Why  are  the  intervals  from  sunrise  to  noon  and  from  noon  to 
sunset  usually  unequal  as  given  in  the  almanac  ?     (For  example,  see 
Feb.  20th  and  Nov.  20th.) 

26.  If  the  earth  were  to  shrink  to  half  its  present  diameter,  what 
would  be  its  mean  density  ? 

27.  Is  it  absolutely  necessary,  as  often  stated,  to  know  the  diameter 
of  the  earth  in  order  to  find  the  distance  of  the  sun  from  the  earth  ? 

28.  How  will  a  projectile  fired  horizontally  on  the  earth  deviate 
from  the  line  it  would  follow  if  the  earth  did  not  rotate  on  its  axis  ? 

29.  If  the  earth  were  to  contract  in  diameter,  how  would  the  weight 
of  bodies  on  its  surface  be  affected  ? 

30.  What  keeps  up  the  speed  of  the  earth  in  its  motion  around  the 
sun? 


334  APPENDIX. 

31.  Why  is  the  sidereal  month  shorter  than  the  synodic? 

32.  Does  the  moon  rise  every  day  of  the  month  ? 

33.  If  the  moon  rises  at  11.45  Tuesday  night,  when  will  it  rise 
next? 

34.  How  many  times  does  the  moon  turn  on  its  axis  in  a  year  ? 

35.  What  determines  the  direction  of  the  horns  of  the  moon  ? 

36.  Does  the  earth  rise  and  set  for  an  observer  on  the  moon  ?  If  so, 
at  what  intervals  ? 

37.  How  do  we  know  that  the  moon  is  not  self-luminous  ? 

38.  How  do  we  know  that  there  is  no  water  on  the  moon  ? 

39.  How  much  information  does  the  spectroscope  give  us  about  the 
moon  ? 

40.  What  conditions  must  concur  to  produce  a  lunar  eclipse  ? 

41.  Can  an  eclipse  of  the  rnoon  occur  in  the  daytime  ? 

42.  Why  can  there  not  be  an  annular  eclipse  of  the  moon  ? 

43.  Which  are  most  frequent  at  New  York,  solar  eclipses  or  lunar? 

44.  Can  an  occultation  of  Venus  by  the  moon  occur  during  a  lunar 
eclipse  ?    Would  an  occultation  of  Jupiter  be  possible  under  the  same 
circumstances  ? 

45.  Which  of  the  heavenly  bodies  are  not  self-luminous  ? 

46.  When  is  a  planet  an  evening  star  ? 

47.  What  planets  have  synodic  periods  longer  than  their  sidereal 
periods  ? 

48.  When  a  planet  is  at  its  least  distance  from  the  earth,  what  is 
its  apparent  motion  in  right  ascension  ? 

49.  A  planet  is  seen  120°  distant  from  the  sun ;  is  it  an  inferior  or 
a  superior  planet  ? 

50.  Can  there  be  a  transit  of  Mars  across  the  sun's  disc  ? 

51.  When  Jupiter  is  visible  in  the  evening,  do  the  shadows  of  the 
satellites  precede  or  follow  the  satellites  themselves  as  they  cross  the 
planet's  disc  ? 

52.  What  would  be  the  length  of  the  month  if  the  moon  were  four 
times  as  far  away  as  now  ?     (Apply  Kepler's  third  law.) 

53.  What  is  the  distance  from  the  sun  of  an  asteroid  which  has  a 
period  of  eight  years  ?     (Kepler's  third  law.) 

54.  Upon  what  circumstances  does  the  apparent  length  of  a  comet's 
tail  depend  ? 

55.  How  can  the  distance  of  a  meteor  from  the  observer,  and  its 
height  above  the  earth,  be  determined  ? 


SUGGESTIVE  QUESTIONS.  335 

56.  What  heavenly  bodies  are  not  included  in  the  solar  system? 

57.  How  do  we  know  tiiat  stars  are  suns  ?     How  much  is  meant  by 
the  assertion  that  they  are  ? 

58.  Suppose  that  in  attempting  to  measure  the  parallax  of  a  bright 
star  by  the  differential  method  (Art.  443)  it  should  turn  out  that  the 
small  star  taken  as  the  point  to  measure  from,  and  supposed  to  be  far 
beyond  the  bright  one,  should  really  prove  to  be  nearer.     How  would 
the  measures  show  the  fact  ? 

59.  If  Alpha  Centauri  were  to  travel  straight  towards  the  sun  with 
a  uniform  velocity  equal  to  that  of  the  earth  in  its  orbit,  how  long 
would  the  journey  take,  on  the  assumption  that  the  star's  parallax  is 
0".75? 

60.  If  Altair  were  ten  times  as  distant  from  us,  what  would  be  its 
apparent   "magnitude"?      What,  if  it  were   a  thousand   times   as 
remote?     (See   Arts.   436,   437;    and   remember  that  the   apparent 
brightness  varies  inversely  with  the  square  of  the  distance.) 


TABLES  OF  ASTRONOMICAL  DATA. 


TABLES.  339 

TABLE   I.  — ASTRONOMICAL   CONSTANTS. 
TIME  CONSTANTS. 

The  sidereal  day       =  23h  56m  48.090  of  mean  solar  time. 
The  mean  solar  day  =  24h  3m  56s. 556  of  sidereal  time. 

To  reduce  a  time  interval  expressed  in  units  of  mean  solar 
time  to  units  of  sidereal  time,  multiply  by  1.00273791;  Log.  of 
0.00273791  =[7.4374191]. 

To  reduce  a  time  interval  expressed  in  units  of  sidereal 
time  to  units  of  mean  solar  time,  multiply  by  0.99726957  = 
(1  -  0.00273043)  ;  Log.  0.00273043  =  [7.4362316]. 

Tropical  year  (Leverrier,  reduced  to  1900),  365d   5h  48m  458.51. 
Sidereal  year  "  "  "       365     6     9      8.97. 

Anomalistic  year      "  «  "       365     6   13    48.09. 

Mean  synodical  month  (new  moon  to  new),  29d  12h  44m  2s. 684. 

Sidereal  month, 27     7   43   11.545. 

Tropical  month  (equinox  to  equinox) ,  .27  7  43  4.68. 
Anomalistic  month  (perigee  to  perigee), .  27  13  18  37.44. 
Nodical  month  (node  to  node),  .  .  27  5  5  35.81. 


Obliquity  of  the  ecliptic  (Leverrier), 

23°  27'  08".0  -  0".4757  (t  - 1900). 

Constant  of  precession  (Struve), 

50".264  +  0".000227  (t  -1900). 

Constant  of  nutation  (Peters),  9".223. 

Constant  of  aberration  (Nyr6n),  20".492. 


Equatorial  semi-diameter  of  the  earth  (Clarke's  spheroid  of 
1878) ,  —    20  926  202 feet  =  6  378 190  metres  =  3963.296  miles. 

Polar  semi-diameter,  — 

20  854  895 feet  =  6  356  456  metres  =  3949.790  mUefl. 
Ellipticity,  or  Polar  Compression,  29s.46- 


340 


APPENDIX. 


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O  CO         T* 


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O  (N  00  rH 
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COdrHrH 


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5gd 

111 


13 


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s.i^ 
ft-S 


IS 

i 


s 


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oo-2 

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t-    P    OJ   ^ 


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i-ft 

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© 


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111! 


TABLES. 


341 


. 

%   jg 

5-2 

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rH        to*     Tr1         CO     £J     CO     rH        tO     O 
rH        rH     tO        CO     "^     CO     rH 

co      ^    ^      t,    co    c<,    «M      ^    eo 

tL      t~to      oow110®      <NOO 

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d                                                     ^ 

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Discovery. 

1 

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ft  -•  s  1  •§  fi  I  s  w  :  1 

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342 


APPENDIX. 


TABLE   IV.  — THE   PRINCIPAL  VARIABLE    STARS. 

A  selection  from  S.  C.  Chandler's  catalogue  of  225  variables  (Astronomical  Journal, 
Sept.,  1888),  containing  such  as,  at  the  maximum,  are  easily  visible  to  the  naked  eye,  have 
a  range  of  variation  exceeding  half  a  magnitude,  and  can  be  seen  in  the  United  States. 


1 

NAME. 

Place,  1900. 

Range  of 
Variation. 

Period  (days). 

Remarks. 

a 

1 

h       m 

1 

R  Andromedae 

0    18.8 

+  38°   1' 

5.6  to  13 

411.2 

(Mira.    Varia- 

2 

oCeti.     .    .    . 

2    14.3 

-  3  26 

1.7      9.5 

331.3363 

|  tions  in  length 

3 
4 

p  Persei  .    .     . 
/3  Persei  .    .     . 

2    58.7 
3      1.6 

+  38  27 
+  40  34 

3.4      4.2 
2.3      3.5 

33 
2*  20h  48*  55'.43 

(  of  period. 
(  Algol.    Period 
\  now  shortening. 

5 

ATauri  .    .    . 

3    55.1 

+  12  12 

3.4      4.2 

3d  22»>  52m  12" 

(  Algol  type,  but 

6 

«  Aurigae     .    . 

4    54.8 

+  43  41 

3         4.5 

Irregular 

\  irregular 

7 

a  Orionis     .     . 

5    49.7 

+   7  23 

1         1.6 

196  ? 

Irregular. 

8 

i)  Geminorum  . 

6      8.8 

+  22  32 

3.2      4.2 

229.1 

9 

£  Geminorum  . 

6    58.2 

+  20  43 

3.7      4.5 

10*    3h  4im  3Q8 

10 

RCanisMaj.  . 

7    14.9 

-16  12 

5.9      6.7 

Id    3h  15""  55" 

Algol  type. 

11 

R  Leonis     .    . 

9    42.2 

+  11  54 

5.2    10 

312.87 

12 

U  Hydras    .    . 

10    32.6 

-12  52 

4.5      6.3 

194.65 

13 

R  Hydrse    .     . 

13    24.2 

-22  46 

3.5      9.7 

496.91 

Period  short'ing 

14 

fi  Librae  .    .    . 

14    55.6 

-87 

5.0      6.2 

2d  7h  5im  22^.8 

Algol  type. 

15 

R  Coronse  .     . 

15    44.4 

+  28  28 

5.8    13 

Irregular 

16 

R  Serpentis     . 

15    46.1 

+  15  26 

5.6    13 

357.6 

17 

a  Herculis  .    . 

17    10.1 

+  14  30 

3.1      3.9 

Two  or  three  mon 

ths,  but  very  irreg. 

18 

U  Ophiuchi     . 

17    11.5 

+   1  19 

6.0      6.7 

20h    7m  418.6 

19 

X  Sagittarii     . 

17    41.3 

-27  48 

4         6 

7.01185 

20 

W  Sagittarii    . 

17    58.6 

-29  35 

5         6.5 

7.59445 

21 

R  Scuti  .    .    . 

18    42.1 

-   5  49 

4.7      9 

71.10 

(  Secondary  mini- 

22 

/SLyrae  .    .    . 

18    46.4 

+  33  15 

3.4      4.5 

12d  21»>  46-°  58'.3 

J  mum  about  mid- 

23 

X  Cygni  .     .    . 

19    46.7 

+  32  40 

4.0    13.5 

406.045 

(  way. 
Period  length'ng 

24 

7)  Aquilro    .    . 

19    47.4 

+   0  45 

3.5      4.7 

7d    4h  i4m    o».0 

25 

S  Sagittse     .     . 

19    51.4 

+  16  22 

5.6      6.4 

8*    9»>  llm 

26 

T  Vulpeculaa  . 

20    47.2 

+  27   52 

5.5      6.5 

4d  iQh  29"> 

27 

TCephei    .    . 

21      8.2 

+  68     5 

5.6      9.9 

383.20 

28 

/u.  Cephei     .    . 

21    40.4 

+  58  19 

4         5 

432? 

29 

6  Cephei      .     . 

22    25.4 

+  57  54 

3.7      4.9 

5*    8»>  47"  39«.97 

30 

pPegasi.    .    . 

22    58.9 

+  27  32 

2.2      2.7 

Irregular 

31 

R  Cassiopeiae  . 

23    53.3 

+  50  50 

4.8    12 

429.00 

TABLES. 


343 


TABLE  V.  — STELLAR  PARALLAXES  AND   PROPER   MOTIONS. 

(From  Oudeman's  Table,  Ast.  Nach.,  Aug.,  1889.) 


No. 

NAME. 

Mag. 

Proper  Motion. 

Annual 
Parallax. 

Distance 
Light  Years. 

1 

a  Centauri     . 

0.7 

3".67 

0".75 

4 

2 

LI.  21185  .     . 

6.9 

4.75 

0.50 

6.5 

3 

61  Cygni  .     . 

5.1 

5.16 

0.40 

8 

4 

Sirius  .     .     . 

-1.4 

1.31 

0.39 

8.3 

5 

22398.     .     . 

8.2 

2.40 

0.35 

9.3 

6 

LI.  9352    .     . 

7.5 

6.96 

0.28 

12 

7 

Procyon    .     . 

0.5 

1.25 

0.27 

12.3 

8 

LI.  21258  .     . 

8.5 

4.40 

0.26 

12.5 

9 

Altair  .     .     . 

1.0 

0.65 

0.20 

16.3 

10 

e  Indi  .     .     . 

5.2 

4.60 

0.20 

16.3 

11 

o2  Eridani 

4.5 

4.05 

0.19 

17 

12 

Vega    .    .     . 

0.2 

0.36 

0.16 

20 

13 

/?  Cassiopeiae, 

2.4 

0.55 

0.16 

20 

14 

70  Ophiuclii  . 

4.1 

1.13 

0.15 

21 

15 

e  Eridani  .     . 

4.4 

3.03 

0.14 

23 

16 

Aldebaran 

1.0 

0.19 

0.12 

27 

17 

Capella     .     . 

0.2 

0.43 

0.11 

29 

18 

Kegulus    .     . 

1.4 

0.27 

0.10 

32 

19 

Polaris      .     . 

2.1 

0.05 

0.07 

47 

These  are  not  all  the  stars  upon  Oudeman's  list  which  are  given  as  hav- 
ing parallaxes  exceeding  0".l ;  but  they  are  probably  the  best  determined 
ones. 


THE   GEEEK   ALPHABET. 


Letters. 

Name. 

Letters. 

Name. 

A,  a, 

Alpha. 

I,  i, 

Iota. 

B,  ft 

Beta. 

K,    K, 

Kappa. 

r,  y, 

Gamma. 

A,  X, 

Lambda. 

A,  8, 

Delta. 

M,.JA, 

Mu. 

E,  c, 

Epsilon. 

N,  v, 

Nu. 

z,  t 

Zeta. 

H,*, 

Xi. 

H,  77, 

Eta. 

0,o, 

Omicron. 

©,  0,  *, 

Theta. 

H,  7T,  TO, 

Pi. 

Letters.  Name. 

P,  P)  &  Kho. 

2,  o-,  ?,  Sigma. 

T,  T,  Tau. 

Y,  v,  Upsilon 

$,  ^>,  Phi. 

X,  x,  Chi. 

^,  \[r,  Psi. 

O,  w,  Omega. 


MISCELLANEOUS   SYMBOLS. 

6 ,  Conjunction.  A.R.,  or  a,  Eight  Ascension. 

D,  Quadrature.  Decl.,  or  8,  Declination. 

<?,  Opposition.  A,  Longitude  (Celestial). 

&,  Ascending  Node.  /?,  Latitude  (Celestial). 

£5?  Descending  Node.  <£,  Latitude  (Terrestrial). 

<o,  Angle  between  line  of  .nodes  and  line  of  apsides  j  also 
the  obliquity  of  the  ecliptic. 

344 


INDEX 


INDEX. 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  to  pages.] 


A. 

Aberration,  of  light,  435 ;  determining 
distance  of  sun,  436. 

Absolute  scale  of  star  magnitudes,  346. 

Acceleration  of  rotation  at  the  sun's 
equator,  163. 

Achromatic  telescope,  406,  407. 

ADAMS,  J.  C.  (and  LEVERRIBR),  dis- 
covery of  Neptune,  283;  orbit  of  the 
Leonids,  327. 

Aerolite.    See  Meteorite. 

Age  of  the  sun  and  planetary  system, 
193,  397-399. 

Albedo  denned,  149,  235 ;  of  the  moon 
(Zolluer),  149;  of  the  planets  (Z611- 
ner),  242,  247,  253,  268,  276,  281,  285. 

Algol,  or  3  Persei,  40,  351,  358,  360. 

Alphabet,  the  Greek,  page  344. 

Altitude  defined,  11;  parallels  of,  11; 
of  the  pole  equals  latitude,  80. 

Andromeda,  constellation  of,  35 ;  neb- 
ula of,  377,  378,  392,  note;  nebula  of, 
temporary  star  in,  355. 

Andromedes,  or  Bielids,  312,  326. 

Angular  measurements,  units  of,  8. 

Annual  or  heliocentric  parallax  de- 
fined, 343;  methods  of  determining 
it  for  the  stars  by  observation,  441- 
444. 

Annular  eclipses,  201. 

Anomalistic  year,  127. 

Anomalous  phenomena  in  comets,  308 

Apex  of  the  sun's  way,  342. 

Aphelion  defined,  120. 

Apogee  defined,  137. 


Apparent  motion  of  a  planet,  225-229 ; 
motion  of  the  sun,  115-117;  solar 
time,  88. 

Apsides,  line  of,  defined,  120,  137;  of 
the  moon's  orbit,  137. 

Aquarius,  78, 118. 

Aquila,  71. 

Arcs  of  meridian,  measurement  of,  105, 
110. 

Areas,  equal,  law  of,  121, 137,  220. 

Argo  Navis,  51. 

Ariel,  a  satellite  of  Uranus,  282. 

Aries,  first  of,  defined,  17;  constella- 
tion of,  38,  118. 

Asteroids,  or  minor  planets,  260-263. 

Astronomical  constants,  table  of,  page 
339;  day,  beginning  of,  90;  symbols, 
page  344 ;  unit,  —  see  Distance  of  the 
sun. 

Astronomy,  utility  of,  1. 

Atmosphere  of  the  moon,  148 ;  of  Mars, 
253 ;  of  Mercury,  242 ;  of  Venus,  248. 

Attraction  of  gravitation,  its  law, 
220,  221. 

Auriga,  41. 

Axis  of  the  earth,  13,  109;  its  per- 
manence, 109. 

Azimuth  defined,  11. 

B. 

BAYER,  his  system  of  lettering  the 
stars,  24. 

Beginning  of  the  century  (Ceres  dis- 
covered) ,  260 ;  of  the  day,  90,  98. 

BESSEL,  dark    stars,   350,  360;    first 
measures  stellar  parallax,  441, 444. 
347        , 


348 


INDEX. 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  to  pages.} 


Bethlehem,  the  star  of,  355. 

BIKLA'S  comet,  311,  312. 

Bielids,  or  Andromedes,  312,  324,  328. 

Binary  stars,  368-371. 

Bissextile  year,  129. 

BODE'S  law,  219. 

BOND,  W.  C.,  discovery  cf  the  "  gauze 
ring"  of  Saturn,  277;  discovery  of 
Hyperion,  280. 

Bootes,  59. 

BREDICHIN,  his  theory  of  comets'  tails, 
307. 

Brightness  of  comets,  291 ;  of  meteors, 
318;  of  stars,  and  causes  of  differ- 
ence, 345-350. 

BROOKS,  his  comets,  290,  299. 


CAESAR,  JULIUS,  reformation   of   the 

calendar,  129. 
Calendar,  the,  128-130. 
Calory,  the,  denned,  187. 
Camelopardus,  31. 
Canals  of  Mars,  256. 
Cancer,  52, 118. 
Canes  Venatici,  58. 
Canis  Major,  49. 
Canis  Minor,  48. 
Capricornus,  73,  118. 
Capture  theory  of  comets,  298. 
Cardinal  points  denned,  16. 
CARRINGTON,  discovery  of  the  peculiar 

law  of  the  sun's  rotation,  163. 
CASSINI,  J.  D.,   discovers  division  in 

Saturn's  ring,  277. 
Cassiopeia,  28. 
Catalogues  of  stars,  335. 
Celestial   globe   described,  400,  401; 

sphere,  infinite,  6. 
Centaurus,  62. 

Centrifugal  force  due  to  earth's  rota- 
tion, 111. 
Cepheus,  29. 

Ceres,  the  first  of  the  asteroids,  260. 
Cetus,  39. 
CHANDLER,  S.   C.,    identification    of 

Lexell's  comet,  299;   his  catalogue 

of  variable  stars,  361. 

^ 


Changes,  gradual,  in  the  brightness 
of  stars,  353;  on  the  surface  of  the 
moon,  155. 

Chemical  constitution  of  the  sun,  175, 
176. 

Chromosphere  of  the  sun,  180,  194; 
and  prominences  made  visible  by  the 
spectroscope,  182. 

Chronograph,  the,  417. 

Chronometer,  the,  417 ;  longitude  by, 
96,  427. 

Circle,  meridian,  the,  81,  99,  418. 

Circles,  hour,  defined,  15. 

Circumpolar  stars,  latitude  by,  81. 

Civil  day  and  astronomical  day,  90. 

Classification  of  the  planets,  Hum- 
boldt,  217;  of  stellar  spectra,  Secchi, 
363 ;  of  variable  stars,  352. 

Clock,  the  astronomical,  417;  its  rate 
and  error,  92,  93,  417. 

Clusters  of  stars,  376. 

Columba,  45. 

Colures  defined,  117. 

Coma  Berenices,  57. 

Comet,  Biela's,  311,  312;  Donati's,  289; 
Encke's,  293,  311;  Lexell-Brooks, 
299;  Halley's,  293;  of  1882,  313, 
314. 

Comets,  anomalous  phenomena  shown 
by,  308;  attendant  companions,  314; 
brightness  and  visibility,  291;  cap- 
ture theory  of  their  origin,  298;  cen- 
tral stripe  in  tail,  308;  connection 
with  meteors,  327-329;  constitution 
of,  300;  danger  fjjpm,  310;  density 
of,  303;  designation  and  nomencla- 
ture, 290;  dimensions  of,  301 ;  elliptic, 
293, 297 ;  envelopes  in  head,  305;  fam- 
ilies of,  297;  formation  of  the  tail, 
306;  their  light  and  spectra,  304; 
mass  of,  302;  nature  of,  309;  num- 
ber of,  289;  orbits  of,  292,  293;  peri- 
odic, their  origin,  297,  298;  sheath 
of  comet  of  1882,  314;  tails  or  trains, 
300,  306-308;  visitors  to  the  solar 
system,  296. 

Comet-groups,  294. 

Conic  sections,  the,  440. 

Conjunction  defined,  132,  227. 


INDEX. 


849 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  to  pages.] 


Constant,  solar,  defined  and  discussed, 

187. 

Constellations,  the,  4,  333.     (For  de- 
tailed description,  see  Chap.  II.) 
Constitution  of  comets,  300;   of  the 

sun,  194. 
Contraction  of  a  comet  nearing  the 

sun,  301;    of   the  sun,  Helmholtz's 

theory,  192,  396,  397. 
COPERNICUS,  rotation   of   the    earth, 

106 ;  his  system,  230. 
Corona  Borealis,  60. 
Corona,  the  solar,  183-185. 
Coronium,  hypothetical  element  of  the 

corona,  184. 
Correction  or  error  of  a  timepiece,  92, 

427. 

Corvus,  55. 
Cosmogony,  389-396. 
Crater,  55. 
Cygnus,  68. 

D. 

Dark  stars,  350,  360. 

DARWIN,  G.  H.,  demonstrates  that  a 
meteoric  swarm  behaves  like  a  gas- 
eous nebula,  394. 

Day,  beginning  of,  98 ;  civil  and  astro- 
nomical, 90. 

Decimation  defined,  14;  determina- 
tion of,  99,  100 ;  parallels  of,  14. 

Degrees  of  latitude,  length  of,  110. 

Deimos,  a  satellite  of  Mars,  258. 

DE  L'ISLE,  his  method  of  observing  a 
transit  of  Venus,  437,  438. 

Delphinus,  74. 

Density  of  comets,  303;  of  the  earth, 
113;  of  the  moon,  143;  of  the  sun, 
161. 

Designation  and  nomenclature  of 
comets,  290;  and  nomenclature  of 
the  stars,  24,  334 ;  and  nomenclature 
of  variable  stars,  361. 

Diameter  of  a  planet,  how  determined, 
232. 

Difference  of  brightness  in  stars,  its 
causes,  350. 

Diffraction,  telescopic,  408. 

Diffraction  grating,  the,  171,  note. 


Dione,  a  satellite  of  Saturn,  280. 

Disc,  spurious,  of  a  star,  408. 

Displacement  of  spectrum  lines  by 
motion  in  line  of  sight,  179,  341,  373. 

Distance  of  a  body  as  depending  on 
its  parallax,  140;  of  the  moon,  141; 
of  the  nebulae,  382;  of  the  planets 
from  the  sun,  Table  II.,  page  340;  of 
the  stars,  343,  441-444;  of  the  sun, 
by  aberration  of  light,  436;  of  the 
sun,  by  the  equation  of  light,  434; 
of  the  sun,  by  its  parallax,  437. 

Distribution  of  the  nebulae,  382;  of 
the  stars  in  the  heavens,  384;  of  sun 
spots,  169. 

Diurnal  or  geocentric  parallax  defined, 
139 ;  rotation  of  the  heavens,  12. 

DOPPLER'S  principle,  179. 

Double  stars,  366,  367;  optical  and 
physical,  distinguished,  367. 

Draco,  30. 

DRAPER,  H.,  photograph  of  the  nebu- 
la of  Orion,  378 ;  photographs  of  star 
spectra,  364. 

Duration  of  solar  eclipses,  203 ;  prob- 
able, of  the  solar  system,  193,  397- 
399. 

K. 

Earth,  the,  astronomical  facts  relating 
to  it,  102;  its  density,  113;  dimen- 
sions of,  105,  110,  Table  I.;  ellip- 
ticity  or  oblateness  determined,  110; 
its  interior  constitution,  114;  mass, 
113;  orbital  motion  of,  115-122,428; 
its  orbit,  changes  in,  122;  its  rota- 
tion, invariability  of,  108;  its  rota- 
tion, proofs  of,  107;  shadow  of,  its 
dimensions,  196;  surface  area  and 
volume,  112;  velocity  in  its  orbit, 
158. 

Earth-shine  on  the  moon,  147. 

Ebb  defined,  210. 

Eccentricity  of  the  earth's  orbit,  119; 
of  an  ellipse  defined,  119,  429. 

Eclipses,  frequency  of,  206;  of  Jupi- 
ter's satellites,  273;  lunar,  197-199; 
Oppolzer's  canon  of,  205 ;  number  in 
a  year,  206;  recurrence  of,  207;  so- 


350 


INDEX. 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  to  pages.] 

lar,  duration'of ,  203 ;  solar,  phenom- 
ena of,  204;  solar,  varieties  of,  total 

annular,  and  partial,  201,  202. 
Ecliptic,  the,  defined,  116;  obliquity 

of,  116;  poles  of,  117. 
Elements,  chemical,  recognized  in  the 

stars,  362;  chemical,  recognized  in 

the  sun,  176;  of  the  planets'  orbits 

Table  II.,  page  340. 
Ellipse,  the,  defined  and  described, 

429,  439,  440. 

Elliptic  comets,  292,  293. 
Ellipticity,  or  oblateness  of  the  earth, 

110. 

Elongation  defined,  132,  227. 
Enceladus,  a  satellite  of  Saturn,  280. 
ENCKE'S  comet,  293,  311. 


Energy 
189. 


of   the   solar  radiation,  188, 


Envelopes  in  the  head  of  a  comet,  305, 

314. 

Equation  of  light,  431^33  ;  of  time,  89. 
Equator,  celestial  or  equinoctial,  de- 

fined, 14. 
Equatorial  acceleration  of  the  sun's 

surface   rotation,  163;    instrument, 

the,  414;    use    in    determining  the 

place  of  a  heavenly  body,  100. 
Equinoctial,  the,  or  celestial  equator, 

defined,  14. 

Equinox,  vernal,  defined,  17,  116. 
Equinoxes,  precession  of,  125,  126. 
Equuleus,  75. 
Eridanus,  44. 
Error  or  correction  of  a  timepiece,  92, 

93,  417. 

Eruptive  prominences  on  the  sun,  182. 
Establishment  of  a  port,  210. 
Eye-pieces,  telescopic,  various  forms, 

409. 


Faculae,  solar,  165. 

Families  of  comets,  297. 

FAYE,  depth  of  sun  spots,  168  ;   modi- 

fication of  the  nebular  hypothesis, 

393. 

Filar  micrometer,  the,  415. 
Flood  tide,  210. 


Form  of  the  earth's  orbit  determined 
428. 

FOUCAULT,  his  pendulum  experiment, 
107. 

FRAUNHOFER  lines  in  the  solar  spec- 
trum, 175,  note. 

Frequency  of  eclipses,  206. 

O. 

Galaxy,  the,  383. 

GALILEO,  his  discovery  of  Jupiter's 
satellites,  272;  discovery  of  phases 
of  Venus,  247 ;  discovery  of  Saturn's 
ring,  277;  discovery  of  sun  spots, 
169;  his  telescope,  402. 

Gemination  of  the  canals  of  Mars,  256. 

Gemini,  47, 118. 

Genesis  of  the  planetary  system,  390, 
391. 

Geocentric  parallax,  139. 

Gibbous  phase  defined,  146. 

Globe,  the  celestial,  described,  400, 401. 

Grating,  diffraction,  171,  note. 

Gravitation,  221,  222. 

Gravity,  at  the  moon's  surface,  143; 
at  the  pole  and  equator  of  the  earth, 
111 ;  at  the  sun's  surface,  161;  super- 
ficial, of  a  planet,  how  determined, 
233. 

Greek  alphabet,  the,  page  344. 

Gregorian  calendar,  the,  130. 

Groups,  cometary,  294. 

Grus,  79. 

Gyroscope  illustrating  the  cause  of  the 
seasons,  123. 

H. 

Habitability  of  Mars,  259. 

HALL,  A.,  discovery  of  the  satellites  of 
Mars,  258. 

HALLEY  discovers  the  proper  motion 
of  stars,  339 ;  his  periodic  comet,  293. 

Harmonic  law,  Kepler's,  220,  430. 

Harvest  and  hunter's  moons,  the,  136. 

Heat  of  meteors,  its  explanation,  318 ; 
from  the  moon,  150;  from  the  stars, 
348,  note;  of  the  sun,  its  constancy, 
191;  of  the  sun,  its  intensity,  190; 
of  the  sun,  its  maintenance,  192;  of 
the  sun,  its  quantity,  187,  189.- 


INDEX. 


351 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not 


Heavenly  bodies  defined  and  enumer- 
ated, 2;  apparent  place  of,  7. 

Heliocentric,  or  annual  parallax,  de- 
fined, 139,  343. 

Helium,  hypothetical  element  in  the 
sun,  181. 

HELMHOLTZ,  his  theory  of  the  sun's 
heat,  192. 

Hercules,  66. 

HERSCHEL,  SIR  J.,  illustration  of  the 
solar  system,  238;  his  names  for  the 
satellites  of  Saturn  and  Uranus,  280, 
282. 

HERSCHEL,  SIR  W.,  discovery  of  Ura- 
nus, 281 ;  his  great  telescope,  412 ;  re- 
lation between  nebulae  and  stars,  395. 

HERSCHELS,  the,  their  star-gauges, 
384. 

HIPPARCHUS,  120,  125,  335,  345. 

Horizon  defined,  rational  and  visible, 
10. 

Horizontal  parallax,  139. 

Hour-angle  defined,  422. 

Hour-Circles  defined,  15. 

Hourly  number  of  meteors,  321. 

HUGGINS,  W.,  observes  spectrum  of 
Mars,  253;  observes  spectrum  of 
Mercury,  242;  observes  spectrum 
of  nebulse,  380;  observes  spectrum 
of  stars,  362;  observes  spectrum  of 
temporary  star  of  1866,  355 ;  spectro- 
scopic  measures  of  star  motions,  341. 

HUMSOLDT,  his  classification  of  the 
planets,  217. 

Hunter's  moon,  the,  136. 

HUYGHENS,  his  discovery  of  Saturn's 
ring,  277;  discovery  of  Titan,  280; 
invention  of  the  pendulum  clock, 
417. 

Hydra,  55. 

Hyperbola,  the,  439,  440. 

Hyperion,  a  satellite  of  Saturn,  280. 


lapetus,  the  remotest  satellite  of  Sat- 
urn, 280. 

Identification  of  the  orbits  of  certain 
comets  and  meteors,  328. 


Illuminating   power  of   a  telescope, 

405. 

Illumination  of  the  moon's  disc  dur- 
ing a  lunar  eclipse,  198. 
Illustration  of  the  proportions  of  the 

solar  system,  238. 
Influence  of  the  moon  on  the  earth, 

151 ;  of  sun  spots  on  the  earth,  170. 
Intensity  of  the  sun's  heat,  189-190; 

of  the  sun's  light,  186. 
Intra-Mercurian  planets,  264. 
Invariability  of  the  earth's  rotation, 

108;  of  the  length  of  the  year  and 

distance  from  the  sun,  122. 
Iron  in  comets,  314;    in    meteorites, 

316;  in  stars,  362;  in  the  sun,  175. 


Julian  calendar,  the,  129. 

Juno,  the  third  asteroid,  260. 

Jupiter  (the  planet) ,  266-271 ;  his  belts, 
red  spot,  and  other  markings,  268, 
271;  his  rotation,  270;  his  satellites, 
and  their  eclipses,  272,  273. 

Jupiter's  family  of  comets,  297. 

K. 

KANT,  a  proposer  of  the  nebular  hy- 
pothesis, 391. 

KEPLER,  his  laws  of  planetary  motion, 
121,  220,  430. 

KIRCHHOFF,  fundamental  principles  of 
spectrum  analysis,  173. 

I*. 

Lacerta,  76. 

LANGLEY,  S.  P.,  his  value  of  the  solar 
constant,  188. 

LAPLACE,  his  capture  theory  of  comets, 
298 ;  his  nebular  hypothesis,  392, 393; 
stability  of  the  solar  system,  288*. 

LASSELL,  his  discovery  of  Ariel  and 
Umbriel,  282;  his  discovery  of  the 
satellite  of  Neptune,  286. 

Latitude  (celestial)  defined,  20;  (ter- 
restrial) defined,  80;  length  of  de- 
grees, 110 ;  methods  of  determining, 
81,  424,426;  variations  of,  109. 

Law,  Bode's,  219 ;  of  the  earth's  orbital 
motion,  121 ;  of  gravitation,  221,  222. 


352 


INDEX. 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  lo  pages.] 


Laws,  Kepler's,  121,  220,  430. 

Leap-year,  129,  130. 

Leo,  53,  118. 

Leo  minor,  54. 

Leonids,  the,  324,  325,  326,  329. 

Lepus,  45. 

LEVERRIER  (and  ADAMS),  discovery 
of  Neptuue,  283 ;  on  the  origin  of  the 
Leonids,  329. 

Libra,  61, 118. 

Librations  of  the  moon,  145. 

LICK  telescope,  the,  412. 

Light,  aberration  of,  435,  436 ;  of  com- 
ets, 291;  equation  of,  the,  432,  433; 
of  the  moon,  149;  of  the  sun,  its  in- 
tensity, 186;  of  the  stars,  348-350; 
velocity  of,  used  to  determine  the 
distance  of  the  sun,  434,  436;  the 
zodiacal,  265. 

Light-ratio  of  the  scale  of  stellar  mag- 
nitude, 346. 

Light-year,  the,  344. 

Local  time,  97 ;  time  from  altitude  of 
the  sun,  427;  time  by  transit  instru- 
ment, 93,  416. 

LOCKYER,  J.  N.,  his  meteoric  hypothe- 
sis, 330,  394;  on  spectra  of  nebulae, 
380. 

Longitude  and  latitude  (celestial)  20; 
(terrestrial),  defined,  94;  (terres- 
trial), methods  of  determining  it, 
95,  96,  427. 

Lunar.    See  Moon. 

Lupus,  62. 

Lynx,  46. 

Lyra,  67. 

91. 

Magnesium  in  nebulae  (Lockyer) ,  380 ; 
in  the  stars,  362 ;  in  the  sun,  176. 

Magnifying  power  of  a  telescope,  404. 

Magnitudes,  star,  345-347 ;  star,  abso- 
lute scale  of,  346;  star,  and  tele- 
scopic power,  347. 

Mars  (the  planet),  251-257;  habita- 
bility  of,  259;  map  of  the  planet, 
257;  satellites,  258;  Schiaparelli's 
observations,  etc.,  256;  telescopic 
aspect,  rotation,  etc.,  253,  254. 


Mass,  definition,  113;  of  comets,  302; 
of  earth,  113;  of  the  moou,  143;  of  a 
planet,  how  determined,  233;  of 
shooting  stars,  how  estimated,  323; 
of  the  sun,  161. 

Masses  of  binary  stars,  371. 

Mazapil,  meteorite  of,  326. 

Mean  and  apparent  places  of  stars, 
336 ;  and  apparent  solar  time,  88-89. 

Melbourne  reflector,  412. 

Mercury  (the  planet),  239-244;  rota- 
tion of,  243;  transits  of,  244. 

Meridian  (celestial)  defined,  11, 15, 16 ; 
(terrestrial),  arcs  of,  measured,  105, 
110;  circle,  the,  81,  99,  418. 

Meteoric  hypothesis  (Lockyer),  330, 
394;  showers,  324-326. 

Meteorite  of  Mazapil,  326. 

Meteorites,  315;  their  constituents, 
316;  their  fall,  315. 

Meteors,  ashes  of,  323;  connection 
with  comets,  327-329 ;  heat  and  light, 
318;  observation  of,  317;  origin  of, 
319 ;  path  and  velocity,  317. 

Micrometer,  the,  415. 

Midnight  sun,  the,  86. 

Milky  Way,  the,  383. 

Mimas,  the  inner  satellite  of  Saturn, 
280. 

Mira  Ceti,  356. 

Missing  and  new  stars,  353. 

Monoceros,  50. 

Month,  sidereal  and  synodic,  133* 

Moon,  its  albedo,  149 ;  its  atmosphere 
discussed,  148;  changes  on  its  sur- 
face, 155;  character  of  its  surface, 
153;  density,  143;  diameter,  surface 
area  and  bulk,  142;  distance  and 
parallax,  141 ;  eclipses  of,  195-199; 
heat,  150;  influence  on  the  earth, 
151;  librations,145;  light  and  albedo, 
149;  map,  154, 156 ;  mass,  density,  and 
gravity,  143;  motion  (in  general), 
132-135 ;  nomenclature  of  objects  on 
surface,  156;  perturbations  of,  134; 
phases,  146;  rotation,  144;  shadow 
of,  200;  surface  structure,  153;  tele- 
scopic appearance,  152;  tempera- 
ture, 150 ;  water  not  present,  148. 


INDEX. 


353 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  to  pages.] 


Motion,  apparent  diurnal,  of  the 
heavens,  12, 13;  of  the  moon,  132-134; 
of  a  planet,  225, 220,  229 ;  of  the  sun, 
115-117;  in  line  of  vision,  effect  on 
spectrum,  179,  341;  of  the  sun  in 
space,  342. 

Motions  of  stars,  338-341. 

Mountains,  lunar,  153, 156. 

Mounting  of  a  telescope,  414. 

Multiple  stars,  375. 

Pi. 

Nadir  defined,  10. 

Nadir-point  of  meridian  circle,  419. 

Names  of  planets,  218 ;  of  satellites  of 
Saturn,  280 ;  of  satellites  of  Uranus, 
282. 

Neap  tide,  210. 

Nebulae,  the,  377-382;  changes  in,  379; 
distance  and  distribution,  382 ;  spec- 
tra of,  380,  381. 

Nebular  hypothesis,  the,  392,  393. 

Negative  eye-pieces,  409. 

Neptune  (the  planet),  283-287. 

NEWCOMB,  S.,  on  the  age  and  duration 
of  the  system,  193 ;  and  MICHELSON, 
the  velocity  of  light,  436. 

NEWTON,  H.  A.,  estimate  of  the  daily 
number  of  meteors,  321 ;  investiga- 
tion of  the  orbit  of  the  Leonids,  327 ; 
nature  of  comets,  309. 

NEWTON,  SIR  ISAAC,  law  of  gravita- 
tion, 221,  222. 

Nodes  of  the  moon's  orbit  and  their 
regression,  134;  of  the  planetary 
orbits,  224. 

NORDENSKIOLD,  ashes  of  meteors,  323. 

Norma,  64. 

Number  of  comets,  289 ;  of  eclipses  in 
a  saros,  207;  of  eclipses  in  a  year, 
206;  of  the  stars,  332. 

NYREN,  his  value  of  the  aberration 
constant,  435. 

O. 

Oberon,  a  satellite  of  Uranus,  282. 

Oblateness  or  ellipticity  of  the  earth 
defined,  110. 

Oblique  sphere,  85. 

Obliquity  of  the  ecliptic,  116. 


OLBERS,  discovers  Pallas  and  Vesta, 
260. 

Ophiuchus,  65. 

OPPOLZER,  his  canon  of  eclipses,  205. 

Opposition  defined,  132,  227. 

Orbit  of  the  earth,  its  form,  etc.,  115, 
122,  428 ;  of  the  moon,  137 ;  parallac- 
tic,  of  a  star,  442. 

Orbital  motion  of  the  earth,  proof  of 
it,  115. 

Orbits  of  binary  stars,  370;  of  comets, 
292 ;  of  the  planets,  223. 

Origin  of  the  asteroids,  263 ;  of  mete- 
ors, 319 ;  of  periodic  comets,  297. 

Orion,  43. 


PALISA,  discovery  of  asteroids,  260. 
Pallas,  the  second  asteroid,  260. 
Parabola,  the,  439,  440. 
Parallax,   annual  or  heliocentric,  of 

the  stars,  139,  343,  441-444 ;  diurnal 

or  geocentric,  139 ;  solar,  by  transit 

of  Venus,  de  1'Isle's  method,  437; 

stellar,  how  determined,  441-444. 
Parallaxes,  stellar,  table  of,  Table  V., 

page  343. 

Parallel  sphere,  84. 
Pegasus,  77. 
Pendulum  used  to  determine  earth's 

form,  111 ;  Foucault,  107. 
Perigee  defined,  137. 
Perihelion  defined,  120. 
Periodicity  of  sun  spots,  169. 
Periods  of  the  Planets,  218;  sidereal 

and  synodic,  133,  162,  228. 
Perseids,  the,  324-326,  328,  329. 
Perseus,  40. 
Perturbations,  lunar,  134 ;  planetary, 

122,  288*. 

PETERS,  asteroid  discoveries,  260. 
Phase  of  Mars,  253. 
Phases  of  Mercury  and  Venus,  242, 

247 ;  of  the  moon,  146 ;  of   Saturn's 

rings,  278. 

Phobos,  a  satellite  of  Mars,  258. 
Phomix,  39. 
Photographic  power  of  eclipsed  moon, 

198;  star-charts,  337;  telescopes,  337. 


354 


INDEX. 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  to  pages.] 


Photographs  of  nebulae,  378 ;  of  star- 
spectra,  341,  364. 

Photography,  solar,  164. 

Photometry,  stellar,  348,  349. 

Photosphere,  the,  165,  194. 

PIAZZI  discovers  Ceres,  260. 

PICKERING,  E.  C.,  photographs  of  star- 
spectra,  364,  373 ;  photometric  obser- 
vations of  eclipses  of  Jupiter's  satel- 
lites, 433;  photometric  measures  of 
stellar  magnitudes,  346. 

Pisces,  36, 118. 

Piscis  Australis,  79. 

Place  of  a  heavenly  body  denned,  7 ; 
of  a  heavenly  body,  how  determined 
by  observation,  99,  100;  of  a  ship, 
how  determined,  426,  427. 

Planet,  albedo  of,  denned,  231,  235; 
apparent  motion  of,  225-229 ;  diame- 
ter and  volume,  how  measured,  232; 
mass  and  density,  how  determined, 
233;  rotation  on  axis  determined, 
234;  satellite  system,  how  investi- 
gated, 236 ;  superficial  gravity  deter- 
mined, 233. 

Planetary  data,  their  relative  accu- 
racy, 237;  system,  its  genesis,  age, 
and  duration,  390-398 ;  its  stability, 
288*. 

Planetoids.    See  Asteroids. 

Planets,  Humboldt's  classification, 
217;  the  list  of, 218;  intra-Mercurian, 
264 ;  minor,  260-263 ;  possibly  attend- 
ing stars,  372;  table  of  elements, 
Appendix,  Table  II.,  page  340;  table 
of  names,  symbols,  etc.,  218. 

Pleiades,  the,  42,  376. 

Pointers,  the,  12, 26. 

Pole  (celestial),  altitude  of,  equals 
latitude,  80;  defined,  13;  effect  of 
precession,  126;  (terrestrial),  diur- 
nal phenomena  near  it,  83. 

Pole-star,  former,  a  Draconis,  126; 
how  recognized,  12. 

Positive  eye-pieces,  409. 

Precession  of  the  equinoxes,  125, 126. 

Prime  vertical,  the,  11. 

PROCTOR,  sun  spots,  168;  theory  of 
comets,  298. 


Prominences,  the  solar,  181,  182,  194. 
Proper  motion  of  stars,  339. 
Ptolemaic  system,  the,  230. 
PTOLEMY,  4,  230. 

Q. 

Quadrature  defined,  132,  227. 
Quiescent  prominences,  182. 


Radiant,  the,  of  a  meteoric  shower, 
324. 

Radius  vector  defined,  120. 

Rate  of  a  timepiece  defined,  417. 

Rectification  of  a  globe,  401. 

Recurrence  of  eclipses,  207. 

Red  spot  of  Jupiter,  271. 

Reflecting  telescope,  the,  411,  413. 

Refracting  telescope,  the,  403-407,  413. 

Refraction,  astronomical,  82. 

Reticle,  the,  410,  416. 

Retrograde  and  retrogression  defined, 
226. 

Reversing  layer,  177. 

Rhea,  a  satellite  of  Saturn,  280. 

Right  ascension  defined,  18,  93;  how 
determined  by  observation,  99, 100. 

Right  sphere,  the,  83. 

Rings  of  Saturn,  the,  277-279. 

ROBERTS.,  photographs  of  nebulae,  378. 

ROSSE,  LORD,  his  great  reflector,  412. 

Rotation,  apparent  diurnal,  of  the 
heavens,  12;  definition  of,  144;  dis- 
tinguished from  revolution,  106,  note ; 
of  earth,  its  effect  on  gravity,  111; 
of  earth,  proofs  of,  107;  of  earth, 
variability  of,  108;  of  the  moon,  144; 
of  the  sun,  162,  163. 

Rotation -period  of  Jupiter,  270;  of 
Mars,  254;  of  Mercury,  243;  of  a 
planet,  how  ascertained,  234;  of 
Saturn,  275;  of  Venus,  249. 


Sagitta,  70. 
Sagittarius,  72, 118. 
Saros,  the,  207. 


INDEX. 


355 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles, 


Satellite  system,  how  investigated, 
236;  systems,  table  of,  Table  III., 
page  341. 

Satellites  of  Jupiter,  272;  of  Mars, 
258;  of  Neptune,  286;  of  Saturn, 
280 ;  of  Uranus,  282. 

Saturn  (the  planet),  274-280. 

Scale  of  stellar  magnitudes,  346. 

SCHIAPARELLI,  identification  of  come- 
tary  and  meteoric  orbits,  328 ;  obser- 
vations of  Mars,  256;  rotation  of 
Mercury  and  Venus,  243,  249. 

SCHWABE,  discovers  periodicity  of  sun 
spots,  169. 

Scintillation  of  the  stars,  365. 

Scorpio,  63,  118. 

Sea,  position  at,  how  found,  426, 427. 

Seasons,  explanation  of,  123-124. 

SECCHI,  on  stellar  spectra,  363;  on 
sun  spots,  168. 

Secondary  spectrum  of  achromatic 
object-glass,  407. 

Serpens,  65. 

Serpentarius,  65. 

Sextant,  the,  420,  421. 

Shadow  of  the  earth,  its  dimensions, 
196;  of  the  moon,  its  dimensions, 
200 ;  of  the  moon,  its  velocity,  203. 

Ship  at  sea,  determination  of  its  posi- 
tion, 426,  427. 

Shooting  stars  (see  also  Meteors)  320- 
324;  ashes  of,  323;  brightness  of, 
323;  elevation  and  path,  322;  mass 
of,  323;  materials  of,  323;  nature  of, 
320 ;  number,  daily  and  hourly,  321 ; 
radiant,  324;  showers  of,  324-326; 
spectrum  of,  323 ;  velocity  of,  322. 

Showers,  meteoric,  324-326. 

Sidereal  and  synodic  months,  133 ;  and 
synodic  periods  of  planets,  228 ;  time 
defined,  91;  year,  127. 

Signs  of  the  zodiac,  118 ;  effect  of  pre- 
cession on  them,  126. 

Sirius,  its  companion,  369;  light  com- 
pared with  that  of  the  sun,  349;  its 
mass  compared  with  that  of  the  sun, 
370. 

Solar  constant,  the,  187;  parallax,  158 ; 
time,  mean  and  apparent,  88,  89. 


Solstice  defined,  117. 

SOSIGENES  and  the  calendar,  129. 

Spectroscope,  its  principle  and  con- 
struction, 171, 172 ;  slitless,  364,  445 ; 
used  to  observe  the  solar  promi- 
nences, 182 ;  used  to  measure  motions 
in  line  of  sight,  178,  179,  341,  373, 
374. 

Spectrum  of  the  chromosphere  and 
prominences,  181 ;  of  comets  in  gen- 
eral, 304;  of  the  comet  of  1882,  314; 
of  meteors,  323;  of  nebulae,  380, 
381;  of  a  shooting  star,  323;  of 
stars,  362-364 ;  the  solar,  172-175 ;  of 
the  solar  corona,  184 ;  of  a  sun  spot, 
178. 

Spectrum  analysis,  fundamental  prin- 
ciples, 173. 

Speculum  of  a  reflecting  telescope, 
411. 

Sphere,  celestial,  the,  6;  doctrine  of 
the,  9-20. 

Spots,  solar.    See  Sun  spots. 

Spring  tide  defined,  210. 

Stability  of  the  planetary  system,  288*. 

Standard  time,  97. 

Stars,  binary,  368-371;  catalogues  of, 
335 ;  charts  of,  337 ;  clusters  of,  376 ; 
dark,  350,  360 ;  designation  and  no- 
menclature, 24,  334;  dimensions  of, 
351,  360;  distance  of,  343,  344;  distri- 
bution of,  384;  double,  366,  367; 
gravitation  among  them,  368,  371, 
386 ;  heat  from  them,  348,  note ;  light 
of  certain  stars  compared  with  sun- 
light, 348,  349;  magnitudes  and 
brightness,  345-350;  mean  and  ap- 
parent places  of,  336;  missing  and 
new,  353 ;  motions  of,  338-342 ;  mul- 
tiple, 375;  new,  353;  number  of, 
332 ;  parallax  of,  343, 441^44 ;  Table 
V.,  page  343;  shooting  (see  Shoot- 
ing stars,  also  Meteors) ;  spectra  of, 
362-364;  system  of  the,  386;  tem- 
porary, 355;  total  amount  of  light 
from  the,  348;  twinkling  of,  365; 
variable,  352-361 ;  Table  IV.,  page 
342. 

Star- gauges  of  the  Herschels,  384. 


356 


INDEX. 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  no 


Starlight,  its  total  amount,  348. 

Stellar  parallaxes,  table  of,  Table  V., 
page  343 ;  photometry,  348,  349. 

Structure  of  the  stellar  universe,  385. 

Sun,  the  age  and  duration  of,  193,  397, 
398 ;  apparent  motion  in  the  heavens, 
115-117;  its  chromosphere,  180;  its 
constitution,  194;  its  corona,  183- 
185 ;  its  density,  161 ;  dimensions  of, 
160;  distance  of,  158,  159,  434-438; 
elements  recognized  in  it,  176 ;  f  ac- 
ulae,  165 ;  gravity  on  its  surface,  161 ; 
heat  of,  quantity,  intensity,  and 
maintenance,  187-192;  light  of,  its 
intensity,  186 ;  mass  of,  161 ;  motion 
in  space,  342;  parallax  of,  159; 
prominences,  181, 182, 194;  reversing 
layer,  the,  177,  194 ;  rotation  of,  162, 
163 ;  spectrum  of,  172,  175 ;  temper- 
ature of,  190;  temperature  dimin- 
ishing, Lockyer,  396,  note. 

Sun  spots,  appearance  and  nature, 
166, 170 ;  cause  of,  168 ;  distribution 
of,  169 ;  influence  on  the  earth,  170 ; 
periodicity  of,  169 ;  spectrum  of,  178. 

Superficial  gravity  of  a  planet,  how 
determined,  233. 

Surface  structure  of  the  moon,  153, 
154. 

Swarms,  meteoric,  324-329. 

Synodic  and  sidereal  months,  133 ;  and 
sidereal  periods  of  planets,  228. 

System,  planetary,  its  age  and  dura- 
tion, 397-399;  its  genesis  and  evo- 
lution, 390-393;  its  stability,  288*; 
stellar,  its  probable  nature,  386-388. 

Syzygy  denned,  132. 

X. 

Tables,  astronomical  constants,  Table 
I.,  page  339;  astronomical  symbols, 
page  344;  binary  stars,  orbits  and 
masses,  370;  Bode's  law,  219;  con- 
stellations, showing  place  in  heavens, 
page  54 ;  Greek  alphabet,  page  344 ; 
moon,  names  of  principal  objects, 
155;  planet's  elements,  Table  II., 
page  340 ;  planet's  names,  distances, 


etc.,  approximate,  218;  satellite  sys- 
tems, Table  III.,  page  341;  stellar 
parallaxes  and  proper  motions,  Table 
V.,  page  343;  variable  stars,  Table 
IV.,  page  342. 

Tails  of  comets,  300,  301,  305-308. 

Taurus,  42. 

Telegraph,  longitude  by,  95. 

Telescope,  achromatic,  406,  407;  eye- 
pieces of,  409 ;  general  principles  of, 
402;  illuminating  power,  405;  mag- 
nifying power,  404;  magnitude  of 
stars  visible  with  a  given  aperture, 
347;  mounting  of,  414;  reflecting, 
411 ;  simple  refracting,  403. 

Telescopes,  great,  412. 

Temperature  of  the  moon,  150;  of  the 
sun,  190. 

Temporary  stars,  355. 

Terminator,  the,  defined  and  described, 
146. 

Tethys,  a  satellite  of  Saturn,  280. 

THOMSON,  SIB  W.,  the  internal  heat  of 
the  earth,  396 ;  the  heat  of  meteors, 
318 ;  the  rigidity  of  the  earth,  114. 

Tidal-wave,  course  of,  213. 

Tides,  the  definitions  relating  to,  210; 
due  mainly  to  moon's  action,  209; 
explanation  of,  208,  209,  211,  212; 
height  of,  214 ;  motion  of,  211, 213 ;  in 
rivers,  215. 

Time,  equation  of,  89 ;  local,  from  sun's 
altitude,  427;  methods  of  determin- 
ing, 92,  93,  427;  relation  to  hour- 
angle,  422 ;  sidereal,  defined,  91 ; 
solar  — mean  and  apparent,  88,  89; 
standard,  defined,  97. 

Titan,  satellite  of  Saturn,  280. 

Titania,  satellite  of  Uranus,  282. 

Total  and  annular  eclipses,  201. 

Trains  of  meteors,  315. 

Transit  or  meridian  circle,  81,  99,  418. 

Transit  instrument,  the,  92,  416. 

Transits  of  Mercury,  244;  of  Venus, 
250. 

Triangulum,  37. 

Tropical  year,  the,  127. 

Twinkling  of  the  stars,  365. 

TYCHO  BRAKE,  his  temporary  star,  355. 


357 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  articles,  not  to  pages.] 

U.  Volcanoes  on  the  moon,  153. 

Vulcan,  the  hypothetical  intra-Mercu- 

rian  planet,  264. 
Vulpecula,  69. 


Ultra-Neptunian  planet,  288. 
Umbriel,  a  satellite  of  Uranus,  282. 
Universe,  stellar,  its  structure,  385. 
Uranography  denned,  5. 
Uranolith,  or  Uranolite.    See  Meteor- 
ite. 

Uranus  (the  planet),  281,  282. 
Ursa  Major,  26. 
Ursa  Minor,  27. 
Utility  of  astronomy,  1. 


Vanishing  point,  6,  note. 

Variable  stars,  352-361;  table  of, 
Table  IV.,  page  342. 

Velocity  of  earth  in  its  orbit,  102,  158 ; 
of  light,  436;  of  moon's  shadow, 
203;  of  meteors  and  shooting  stars, 
317,  322 ;  of  star  motions,  340,  341. 

Venus  (the  planet),  245-250;  phases 
of,  247 ;  transits  of,  250. 

Vernal  equinox,  the,  17,  36, 116. 

Vertical  circles,  11. 

Vesta,  the  fourth  asteroid,  260. 

Virgo,  56, 118. 

Visible  horizon  denned,  10. 

VOGBL,  H.  C.,  spectroscopic  determina- 
tion of  star  motions  in  the  line  of 
sight,  341;  spectroscopic  observa- 
tions of  Algol  and  Spica,  360,  374. 


W. 

Water  absent  from  the  moon,  148. 
Wave-length  of  a  light-ray  affected 

by  motion  in  the  line  of  sight,  Dop- 

pler's  principle,  179,  341. 
Wave,  tidal,  its  course,  213. 
Way,  the  sun's,  342. 
Weather,  the  moon's  influence  on,  151. 
Weight,   loss  of,  between   pole   and 

equator,  111. 

Y. 

Year,  the  sidereal,  tropical,  and  anom- 
alistic, 127,  and  Table  I.,  page  339. 


Zenith,  the,  denned,  10. 
Zenith  distance  denned,  11. 
Zero-points  of  the  meridian  circle,  418, 

419. 
Zodiac,  the,  and  its  signs,  118 ;  its  signs 

as  affected  by  precession,  126. 
Zodiacal  light,  the,  265. 
ZOLLNER,  determination  of    planets' 

albedoes,  242,  247,  253,  268,  276,  281, 

285 ;  measurement  of  moonlight,  149 ; 

measures  of  light  of  stars,  348. 


